x y : Nat
⊢ x + y = Nat.add y x
x y : Nat
⊢ x + y = Nat.add y x
x y : Nat
⊢ Nat.add x y = Nat.add y x
x y : Nat
⊢ f x (Nat.add x y) y = y + x
x y : Nat
⊢ x + y
case h.h
a b : Nat
⊢ 0 + a + b
a b : Nat
⊢ a + b
case h.h
a b : Nat
⊢ 0 + a + b
case h
p : Nat → Prop
h : ∀ (a : Nat), p a
x : Nat
⊢ p (id (0 + x))
p : Nat → Prop
h : ∀ (a : Nat), p a
x : Nat
⊢ id (0 + x)
p : Nat → Prop
h : ∀ (a : Nat), p a
x : Nat
⊢ 0 + x
case h₁
p : Prop
x : Nat
⊢ x = x → p
p : Prop
x : Nat
⊢ (True → p) → p
case h
x : Nat
⊢ 0 + x
p : Prop
x : Nat
⊢ (True → p) → p
x y : Nat
f : Nat → Nat → Nat
g : Nat → Nat
h₁ : ∀ (z : Nat), f z z = z
h₂ : ∀ (x y : Nat), f (g x) (g y) = y
⊢ f (g y) (f (g x) (g (0 + x))) = x
x y : Nat
f : Nat → Nat → Nat
g : Nat → Nat
h₁ : ∀ (z : Nat), f z z = z
h₂ : ∀ (x y : Nat), f (g x) (g y) = y
⊢ f (g y) (f (g x) (g x)) = x
x y : Nat
h : y = 0
⊢ y + x
conv1.lean:139:10-139:13: error: invalid 'lhs' conv tactic, application has only 1 (nondependent) argument(s)
conv1.lean:142:10-142:15: error: invalid 'arg' conv tactic, application has only 1 (nondependent) argument(s)
conv1.lean:145:10-145:13: error: invalid 'congr' conv tactic, application or implication expected
  p
p : Nat → Prop
x y : Nat
h1 : y = 0
h2 : p x
⊢ y + x