Created
March 12, 2021 05:00
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Binary Nat thing from https://twitter.com/TaliaRinger/status/1370213824716963840
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| open import Data.Nat.Binary | |
| open import Relation.Binary.PropositionalEquality | |
| plus-zero : ∀ n -> (n + zero) ≡ n | |
| plus-zero zero = refl | |
| plus-zero 2[1+ n ] = refl | |
| plus-zero 1+[2 n ] = refl | |
| plus-suc : ∀ n m -> suc (n + m) ≡ n + (suc m) | |
| plus-suc zero m = refl | |
| plus-suc 2[1+ n ] zero rewrite plus-zero n = refl | |
| plus-suc 1+[2 n ] zero rewrite plus-zero n = refl | |
| plus-suc 2[1+ n ] 2[1+ m ] rewrite plus-suc n m = refl | |
| plus-suc 2[1+ n ] 1+[2 m ] = refl | |
| plus-suc 1+[2 n ] 2[1+ m ] rewrite plus-suc n m = refl | |
| plus-suc 1+[2 n ] 1+[2 m ] = refl |
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