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Tactic state
No goals
Goals accomplished!
Tactic state
1 goal
Coin HotWater : Prop
Noodles : Sort ?u.29
noodleVendingMachine : Coin → HotWater → Noodles
coinAndHotWater : Coin ∧ HotWater
⊢ Noodles
Tactic state
1 goal
Coin HotWater : Prop
Noodles : Sort ?u.29
noodleVendingMachine : Coin → HotWater → Noodles
⊢ Coin ∧ HotWater → Noodles
Tactic state
1 goal
Coin HotWater : Prop
Noodles : Sort ?u.29
⊢ (Coin → HotWater → Noodles) → Coin ∧ HotWater → Noodles
#check rfl
-- rfl.{u} {α : Sort u} {a : α} : a = a
#check 2 + 2 = 4
-- 2 + 2 = 4 : Prop
#check Type
-- Type : Type 1
#check Type 1
-- Type 1 : Type 2
-- ...
#check Nat
-- Nat : Type
#check 3
-- 3 : Nat
example : (P → Q → R) → (P ∧ Q → R) := by
intro h
intro hpq
exact h hpq.left hpq.right