85 lines
1.6 KiB
Text
85 lines
1.6 KiB
Text
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
|
|
p : Nat → Prop
|
|
x y : Nat
|
|
h1 : y = 0
|
|
h2 : p x
|
|
| y + x
|
|
j : Fin 5
|
|
p : (n : Nat) → Fin n → Prop
|
|
i : Fin 5
|
|
hp : p 5 i
|
|
hi : j = i
|
|
| j
|
|
p : {x : Nat} → Nat → Prop
|
|
x y : Nat
|
|
h1 : y = 0
|
|
h2 : p x
|
|
| y
|
|
p : {x : Nat} → Nat → Prop
|
|
x y : Nat
|
|
h1 : y = 0
|
|
h2 : p x
|
|
| y
|
|
conv1.lean:166:10-166:13: error: invalid 'lhs' conv tactic, application has only 1 (nondependent) argument(s)
|
|
conv1.lean:169:10-169:15: error: invalid 'arg' conv tactic, application has only 1 (nondependent) argument(s)
|
|
conv1.lean:172:10-172:13: error: invalid 'congr' conv tactic, application or implication expected
|
|
p
|
|
conv1.lean:175:10-175:15: error: cannot select argument with forward dependencies
|