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Canonical terms for the concat function in this blog post: http://spire-lang.org/blog/2014/01/15/modeling-elimination-of-described-types/
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| λ A m n → | |
| ind | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t)) | |
| (λ n₁ xss → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₂ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u₁ c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₂ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → n₃) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq tt | |
| (λ u₂ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| n₂ (proj₁ ih,tt n₂)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c) (proj₂ t,c)) | |
| n₁ m)) | |
| (λ n₁ t,c → | |
| case | |
| (λ t → | |
| (c | |
| : El | |
| (case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t) | |
| (λ n₂ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₂ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₃ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₃)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₃ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₃)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t₂)) | |
| m) | |
| (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₂) | |
| n₁) | |
| → | |
| All | |
| (case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t) | |
| (λ n₂ xss → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t₁ → | |
| (c₁ | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case | |
| (λ t₁ → | |
| (c₁ | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u₁) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (λ u₂ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u₁ c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₂ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → n₄) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq tt | |
| (λ u₂ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₁ n₄ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₃ (proj₁ ih,tt n₃)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| n₂ m)) | |
| n₁ c → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t₁ → | |
| (c₁ | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case | |
| (λ t₁ → | |
| (c₁ | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u₁) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (λ u₂ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u₁ c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₂ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → n₃) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq tt | |
| (λ u₂ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₂ (proj₁ ih,tt n₂)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| n₁ m)) | |
| ((λ q ih → | |
| elimEq (con (here , refl)) | |
| (λ n₂ q₁ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₂ ih₁ → | |
| elimEq tt | |
| (λ u₁ q₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (here , refl)) u q₂) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq tt | |
| (λ u₁ q₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₂ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u₁ c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₂ ih₁ → | |
| elimEq tt | |
| (λ u₂ q₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → n₄) u₁ q₂) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq tt | |
| (λ u₂ q₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₁ n₄ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₃ (proj₁ ih,tt n₃)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| n₂ m)) | |
| (con (here , refl)) n₁ q) | |
| , | |
| (λ n',x,xs,q ih,tt → | |
| elimEq (con (there here , proj₁ n',x,xs,q , refl)) | |
| (λ n₂ q → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₁ ih → | |
| elimEq tt | |
| (λ u₁ q₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (here , refl)) u q₁) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₂ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u₁ c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₁ ih → | |
| elimEq tt | |
| (λ u₂ q₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → n₄) u₁ q₁) | |
| , | |
| (λ n,q₁ ih,tt₂ → | |
| elimEq tt | |
| (λ u₂ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₂ n₄ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₃ (proj₁ ih,tt₁ n₃)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| n₂ m)) | |
| (ind | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| (λ m₁ xs → | |
| (n₂ | |
| : μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| n₂ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → n₃) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| m₁ n₂)) | |
| (λ n₂ t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El | |
| (case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t) | |
| (λ n₃ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₃) | |
| n₂) | |
| → | |
| All | |
| (case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t) | |
| (λ m₁ xs → | |
| (n₃ | |
| : μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₃ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t₁ → | |
| (c₁ | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → n₄) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₁ n₄ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| m₁ n₃)) | |
| n₂ c → | |
| (n₃ | |
| : μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₃ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t₁ → | |
| (c₁ | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → n₄) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₁ n₄ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₂ n₃)) | |
| ((λ q ih → | |
| elimEq (con (here , refl)) | |
| (λ n₃ q₁ → | |
| (n₄ | |
| : μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₅ → | |
| `Arg A (λ _ → `Rec n₅ (`End (con (there here , n₅ , refl))))) | |
| , tt) | |
| t)) | |
| n₄ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₅ → | |
| `Arg A (λ _ → `Rec n₅ (`End (con (there here , n₅ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₂ ih₁ → | |
| elimEq tt | |
| (λ u₁ q₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₅ → n₅) u q₂) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq tt | |
| (λ u₁ q₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₅ → con (there here , proj₁ ih,tt₁ n₅ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₃ n₄)) | |
| (λ n₃ ys → ys) n₂ q) | |
| , | |
| (λ n',x,xs,q₁ ih,tt₁ → | |
| elimEq (con (there here , proj₁ n',x,xs,q₁ , refl)) | |
| (λ n₃ q → | |
| (n₄ | |
| : μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₅ → | |
| `Arg A (λ _ → `Rec n₅ (`End (con (there here , n₅ , refl))))) | |
| , tt) | |
| t)) | |
| n₄ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₅ → | |
| `Arg A (λ _ → `Rec n₅ (`End (con (there here , n₅ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₁ ih → | |
| elimEq tt | |
| (λ u₁ q₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₅ → n₅) u q₁) | |
| , | |
| (λ n,q ih,tt₂ → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₅ → con (there here , proj₁ ih,tt₂ n₅ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₃ n₄)) | |
| (λ n₃ ys → | |
| con | |
| (there here , | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → n₄) u q) | |
| , | |
| (λ n,q ih,tt₂ → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₂ n₄ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| (proj₁ n',x,xs,q₁) n₃ | |
| , proj₁ (proj₂ n',x,xs,q₁) , proj₁ ih,tt₁ n₃ ys , refl)) | |
| n₂ (proj₂ (proj₂ (proj₂ n',x,xs,q₁)))) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| (proj₁ (proj₂ n',x,xs,q)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₁ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq tt | |
| (λ u₁ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₂ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u₁ c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq tt | |
| (λ u₂ q₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → n₃) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₂ → | |
| elimEq tt | |
| (λ u₂ q → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₂ n₃ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₂ (proj₁ ih,tt₁ n₂)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| (proj₁ n',x,xs,q) m) | |
| (proj₁ ih,tt)) | |
| n₁ (proj₂ (proj₂ (proj₂ n',x,xs,q)))) | |
| , tt) | |
| (proj₁ t,c) (proj₂ t,c)) |
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| λ A m n → | |
| ind | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t)) | |
| (λ n₁ xss → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ n₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₂ → con (here , refl)) , | |
| (λ m,q ih,tt n₂ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
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| u → | |
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| ((λ q ih n₃ → con (here , refl)) , | |
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| ind | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u) | |
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| ind | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁ → | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
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| (λ m,q₁ ih,tt₁ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) , | |
| tt) | |
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| tt) | |
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| , tt) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u) | |
| ((λ q₁ ih₁ n₃ → con (here , refl)) , | |
| (λ m,q ih,tt n₃ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt → | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₂) | |
| u₁ c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| ((λ q₁ ih₁ n₄ → n₄) , | |
| (λ m,q₁ ih,tt₁ n₄ → con (there here , proj₁ ih,tt₁ n₄ , refl)) , | |
| tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₃ (proj₁ ih,tt n₃)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| n₂ m)) | |
| q (con (here , refl))) | |
| , | |
| (λ n',xs,xss,q ih,tt → | |
| subst | |
| (λ n₂ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
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| (λ u₁ n₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₃ → con (here , refl)) , | |
| (λ m,q ih,tt₁ n₃ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt → | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| (λ u₁ t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
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| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₂ → | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₂) | |
| u₁ c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
| ((λ q ih n₄ → n₄) , | |
| (λ m,q₁ ih,tt₂ n₄ → con (there here , proj₁ ih,tt₂ n₄ , refl)) , | |
| tt) | |
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| (ind | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| (λ m₁ xs → | |
| (n₂ | |
| : μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
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| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
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| n₂ → | |
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| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
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| (λ t → | |
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| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ n₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₃ → n₃) , | |
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| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| m₁ n₂)) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt)) | |
| (`End (con (here , refl)) , | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
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| , tt) | |
| t) | |
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| t₁)) | |
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| All | |
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| tt) | |
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| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
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| tt) | |
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| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
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| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
| u c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u) | |
| ((λ q ih n₃ → n₃) , | |
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| m₂ n₂)) | |
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| (n₂ | |
| : μ | |
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| tt) | |
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| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt)) | |
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| tt) | |
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| , tt) | |
| t₁)) | |
| n₂ → | |
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| tt)) | |
| (`End (con (here , refl)) , | |
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| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
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| , tt) | |
| t₁)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₂ → | |
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| (λ t₁ → | |
| (c₁ | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (λ u₁ n₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
| u c₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u) | |
| ((λ q ih n₃ → n₃) , | |
| (λ m,q ih,tt₁ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| m₁ n₂)) | |
| ((λ q ih n₂ → | |
| subst | |
| (λ m₂ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ n₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q₁ ih₁ n₃ → n₃) , | |
| (λ m,q ih,tt₁ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| m₂ n₂)) | |
| q) | |
| , | |
| (λ m',x,xs,q ih,tt₁ n₂ ys → | |
| subst | |
| (λ m₂ → | |
| μ | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case | |
| (λ _ → | |
| Desc | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ n₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₃ → n₃) , | |
| (λ m,q ih,tt₂ n₃ → con (there here , proj₁ ih,tt₂ n₃ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| m₂ n₂)) | |
| (proj₂ (proj₂ (proj₂ m',x,xs,q))) | |
| (con | |
| (there here , | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ n₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₃ → n₃) , | |
| (λ m,q ih,tt₂ n₃ → con (there here , proj₁ ih,tt₂ n₃ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| (proj₁ m',x,xs,q) n₂ | |
| , proj₁ (proj₂ m',x,xs,q) , proj₁ ih,tt₁ n₂ ys , refl))) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| (proj₁ (proj₂ n',xs,xss,q)) | |
| (ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₁ n₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₂ → con (here , refl)) , | |
| (λ m,q ih,tt₁ n₂ → | |
| ind | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case | |
| (λ t → | |
| (c | |
| : El (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All (case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t) | |
| (λ u₂ n₃ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₂ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₂) | |
| u₁ c → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → case (λ _ → Desc ⊤) (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| ((λ q ih n₃ → n₃) , | |
| (λ m,q₁ ih,tt₂ n₃ → con (there here , proj₁ ih,tt₂ n₃ , refl)) , | |
| tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| n₂ (proj₁ ih,tt₁ n₂)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| (proj₁ n',xs,xss,q) m) | |
| (proj₁ ih,tt))) | |
| , tt) | |
| (proj₁ t,c) (proj₂ t,c)) |
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| λ A m → | |
| ind | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n → | |
| `Arg | |
| (μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₁ → | |
| `Arg A (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n (`End (con (there here , n , refl))))) | |
| , tt) | |
| t)) | |
| (λ n xss → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| `Arg A (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₁ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₁ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
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| μ ⊤ | |
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| tt) | |
| (λ u₁ t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
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| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| u₁) | |
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| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₂ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₂ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| (λ n₂ → n₂) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₂ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| μ ⊤ | |
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| tt) | |
| (λ n₂ → con (there here , proj₁ ih,tt₁ n₂ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt n₁ (proj₁ ih,tt n₁)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c) (proj₂ t,c)) | |
| tt n m)) | |
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| case ("nil" ∷ "cons" ∷ []) | |
| (λ t → | |
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| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| tt) | |
| (case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
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| (μ ⊤ | |
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| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
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| tt) | |
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| (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
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| , tt) | |
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| All | |
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| , tt) | |
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| (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₁) | |
| (λ n₁ xss → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
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| tt) | |
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| , tt) | |
| t₁)) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| (λ u t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
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| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| u) | |
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| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
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| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t₁ → | |
| (c₁ | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u₁) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₂ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u₁ c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₂ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → n₃) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₂ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₂ (proj₁ ih,tt n₂)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt n₁ m)) | |
| n c → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₁ → | |
| `Arg A (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t₁ → | |
| (c₁ | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t₁ → | |
| (c₁ | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u₁) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₂ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u₁ c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₂ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → n₂) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₂ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → con (there here , proj₁ ih,tt₁ n₂ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₁ (proj₁ ih,tt n₁)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt n m)) | |
| ((λ q ih → | |
| elimEq | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (con (here , refl)) | |
| (λ n₁ q₁ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₂ ih₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q₃ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → con (here , refl)) u q₂) | |
| , | |
| (λ n,q ih,tt → | |
| elimEq ⊤ tt | |
| (λ u₁ q₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₂ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u₁ c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₂ ih₁ → | |
| elimEq ⊤ tt | |
| (λ u₂ q₃ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → n₃) u₁ q₂) | |
| , | |
| (λ n,q₁ ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₂ q₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₂ (proj₁ ih,tt n₂)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt n₁ m)) | |
| (con (here , refl)) n q) | |
| , | |
| (λ n',x,xs,q ih,tt → | |
| elimEq | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (con (there here , proj₁ n',x,xs,q , refl)) | |
| (λ n₁ q → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₁ ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → con (here , refl)) u q₁) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₂ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u₁ c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₁ ih → | |
| elimEq ⊤ tt | |
| (λ u₂ q₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → n₃) u₁ q₁) | |
| , | |
| (λ n,q₁ ih,tt₂ → | |
| elimEq ⊤ tt | |
| (λ u₂ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₂ n₃ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₂ (proj₁ ih,tt₁ n₂)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt n₁ m)) | |
| (ind | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| `Arg A (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t)) | |
| (λ m₁ xs → | |
| (n₁ | |
| : μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| n₁ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → n₂) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → con (there here , proj₁ ih,tt₁ n₂ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt m₁ n₁)) | |
| (λ n₁ t,c₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ t → | |
| (c | |
| : El | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t) | |
| (λ n₂ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₂) | |
| n₁) | |
| → | |
| All | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t) | |
| (λ n₂ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₂) | |
| (λ m₁ xs → | |
| (n₂ | |
| : μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₂ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t₁ → | |
| (c₁ | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → n₃) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt m₁ n₂)) | |
| n₁ c → | |
| (n₂ | |
| : μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₂ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t₁ → | |
| (c₁ | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| u c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → n₃) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₁ n₃ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₁ n₂)) | |
| ((λ q ih → | |
| elimEq | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (con (here , refl)) | |
| (λ n₂ q₁ → | |
| (n₃ | |
| : μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t)) | |
| n₃ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₂ ih₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q₃ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → n₄) u q₂) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₁ n₄ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₂ n₃)) | |
| (λ n₂ ys → ys) n₁ q) | |
| , | |
| (λ n',x,xs,q₁ ih,tt₁ → | |
| elimEq | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (con (there here , proj₁ n',x,xs,q₁ , refl)) | |
| (λ n₂ q → | |
| (n₃ | |
| : μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t)) | |
| n₃ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₄ → | |
| `Arg A (λ _ → `Rec n₄ (`End (con (there here , n₄ , refl))))) | |
| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q₁ ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → n₄) u q₁) | |
| , | |
| (λ n,q ih,tt₂ → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₄ → con (there here , proj₁ ih,tt₂ n₄ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₂ n₃)) | |
| (λ n₂ ys → | |
| con | |
| (there here , | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → n₃) u q) | |
| , | |
| (λ n,q ih,tt₂ → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₃ → con (there here , proj₁ ih,tt₂ n₃ , refl)) u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt (proj₁ n',x,xs,q₁) n₂ | |
| , proj₁ (proj₂ n',x,xs,q₁) , proj₁ ih,tt₁ n₂ ys , refl)) | |
| n₁ (proj₂ (proj₂ (proj₂ n',x,xs,q₁)))) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| m (proj₁ (proj₂ n',x,xs,q)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₁ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₁ → con (here , refl)) u q) | |
| , | |
| (λ n,q ih,tt₁ → | |
| elimEq ⊤ tt | |
| (λ u₁ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₁ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ u₁ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₂ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| u₁ c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| ((λ q ih → | |
| elimEq ⊤ tt | |
| (λ u₂ q₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → n₂) u₁ q) | |
| , | |
| (λ n,q₁ ih,tt₂ → | |
| elimEq ⊤ tt | |
| (λ u₂ q → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ n₂ → con (there here , proj₁ ih,tt₂ n₂ , refl)) u₁ (proj₂ n,q₁)) | |
| , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₁ (proj₁ ih,tt₁ n₁)) | |
| u (proj₂ n,q)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt (proj₁ n',x,xs,q) m) | |
| (proj₁ ih,tt)) | |
| n (proj₂ (proj₂ (proj₂ n',x,xs,q)))) | |
| , tt) | |
| (proj₁ t,c) (proj₂ t,c)) |
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| λ A m → | |
| ind | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n → | |
| `Arg | |
| (μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₁ → | |
| `Arg A (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n (`End (con (there here , n , refl))))) | |
| , tt) | |
| t)) | |
| (λ n xss → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| `Arg A (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ n₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₁ → con (here , refl)) , | |
| (λ m,q ih,tt n₁ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₂ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₂) | |
| u₁ c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| ((λ q ih n₂ → n₂) , | |
| (λ m,q₁ ih,tt₁ n₂ → con (there here , proj₁ ih,tt₁ n₂ , refl)) , | |
| tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt n₁ (proj₁ ih,tt n₁)) | |
| , tt) | |
| (proj₁ t,c) (proj₂ t,c)) | |
| tt n m)) | |
| (λ n t,c → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ t → | |
| (c | |
| : El | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| `Arg | |
| (μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t) | |
| (λ n₁ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg | |
| (μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₂ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₃ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₃)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₃ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₃)) | |
| tt) | |
| (λ n₃ → | |
| `Arg A (λ _ → `Rec n₃ (`End (con (there here , n₃ , refl))))) | |
| , tt) | |
| t₂)) | |
| m) | |
| (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₁) | |
| n) | |
| → | |
| All | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ n₁ → | |
| `Arg | |
| (μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| m) | |
| (λ _ → `Rec n₁ (`End (con (there here , n₁ , refl))))) | |
| , tt) | |
| t) | |
| (λ n₁ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₂ → | |
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| (`End (con (here , refl)) , | |
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| , tt) | |
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| n₁) | |
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| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| (μ ⊤ | |
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| All ⊤ | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| (λ u₁ n₂ → | |
| μ ⊤ | |
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| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
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| μ ⊤ | |
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| μ ⊤ | |
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| u) | |
| ((λ q ih n₂ → con (here , refl)) , | |
| (λ m,q ih,tt n₂ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt → | |
| μ ⊤ | |
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| (λ t₁ → | |
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| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
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| All ⊤ | |
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| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (λ u₂ n₃ → | |
| μ ⊤ | |
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| u₂ → | |
| μ ⊤ | |
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| u₁) | |
| ((λ q ih n₃ → n₃) , | |
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| tt) | |
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| tt)) | |
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| tt) | |
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| (λ _ _ → | |
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| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u) | |
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| All ⊤ | |
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| μ ⊤ | |
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| u) | |
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| (λ m,q ih,tt n₁ → | |
| ind ⊤ | |
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| (λ t₁ → | |
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| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
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| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| (λ u₂ n₂ → | |
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| μ ⊤ | |
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| μ ⊤ | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u₁) | |
| ((λ q ih n₂ → n₂) , | |
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| tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
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| ((λ q ih → | |
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| tt)) | |
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| μ ⊤ | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| u) | |
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| All ⊤ | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| (λ u₁ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| u) | |
| ((λ q₁ ih₁ n₂ → con (here , refl)) , | |
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| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₁) | |
| (λ m₂ xs → | |
| (n₁ | |
| : μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
| Desc | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₁ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
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| (λ _ → | |
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| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t₁ → | |
| (c₁ | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₁ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| u₁) | |
| u c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| u → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| u) | |
| ((λ q ih n₂ → n₂) , | |
| (λ m,q ih,tt₁ n₂ → con (there here , proj₁ ih,tt₁ n₂ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt m₂ n₁)) | |
| m₁ c → | |
| (n₁ | |
| : μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
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| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| tt) | |
| (λ n₂ → | |
| `Arg A (λ _ → `Rec n₂ (`End (con (there here , n₂ , refl))))) | |
| , tt) | |
| t₁)) | |
| n₁ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t₁ → | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
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| , tt) | |
| t₁)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| tt) | |
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| case ("zero" ∷ "suc" ∷ []) | |
| (λ t₁ → | |
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| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂))) | |
| (λ u₁ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₂)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| u₁) | |
| u c₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₂ → | |
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| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| u) | |
| ((λ q ih n₂ → n₂) , | |
| (λ m,q ih,tt₁ n₂ → con (there here , proj₁ ih,tt₁ n₂ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt m₁ n₁)) | |
| ((λ q ih n₁ → | |
| subst | |
| (λ m₂ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
| (λ t → | |
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| (λ _ → | |
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| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
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| tt) | |
| (λ n₂ → | |
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| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
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| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| u₁) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
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| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q₁ ih₁ n₂ → n₂) , | |
| (λ m,q ih,tt₁ n₂ → con (there here , proj₁ ih,tt₁ n₂ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt m₂ n₁)) | |
| q) | |
| , | |
| (λ m',x,xs,q ih,tt₁ n₁ ys → | |
| subst | |
| (λ m₂ → | |
| μ | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (`Arg (Tag ("nil" ∷ "cons" ∷ [])) | |
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| case ("nil" ∷ "cons" ∷ []) | |
| (λ _ → | |
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| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| tt)) | |
| (`End (con (here , refl)) , | |
| `Arg | |
| (μ ⊤ | |
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| tt) | |
| (λ n₂ → | |
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| , tt) | |
| t)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
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| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
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| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
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| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₂ → n₂) , | |
| (λ m,q ih,tt₂ n₂ → con (there here , proj₁ ih,tt₂ n₂ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt m₂ n₁)) | |
| (proj₂ (proj₂ (proj₂ m',x,xs,q))) | |
| (con | |
| (there here , | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₂ → n₂) , | |
| (λ m,q ih,tt₂ n₂ → con (there here , proj₁ ih,tt₂ n₂ , refl)) , tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt (proj₁ m',x,xs,q) n₁ | |
| , proj₁ (proj₂ m',x,xs,q) , proj₁ ih,tt₁ n₁ ys , refl))) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| m (proj₁ (proj₂ n',xs,xss,q)) | |
| (ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u t,c₁ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₁ n₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| u c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u) | |
| ((λ q ih n₁ → con (here , refl)) , | |
| (λ m,q ih,tt₁ n₁ → | |
| ind ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| (λ _ _ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t)) | |
| tt) | |
| (λ u₁ t,c₂ → | |
| case ("zero" ∷ "suc" ∷ []) | |
| (λ t → | |
| (c | |
| : El ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| u₁) | |
| → | |
| All ⊤ | |
| (case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t) | |
| (μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁))) | |
| (λ u₂ n₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₂ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₂) | |
| u₁ c → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁ → | |
| μ ⊤ | |
| (`Arg (Tag ("zero" ∷ "suc" ∷ [])) | |
| (λ t₁ → | |
| case ("zero" ∷ "suc" ∷ []) (λ _ → Desc ⊤) | |
| (`End tt , `Rec tt (`End tt) , tt) t₁)) | |
| u₁) | |
| ((λ q ih n₂ → n₂) , | |
| (λ m,q₁ ih,tt₂ n₂ → con (there here , proj₁ ih,tt₂ n₂ , refl)) , | |
| tt) | |
| (proj₁ t,c₂) (proj₂ t,c₂)) | |
| tt n₁ (proj₁ ih,tt₁ n₁)) | |
| , tt) | |
| (proj₁ t,c₁) (proj₂ t,c₁)) | |
| tt (proj₁ n',xs,xss,q) m) | |
| (proj₁ ih,tt))) | |
| , tt) | |
| (proj₁ t,c) (proj₂ t,c)) |
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