30 lines
746 B
Text
30 lines
746 B
Text
Set: pp::colors
|
|
Set: pp::unicode
|
|
Assumed: f
|
|
Assumed: N
|
|
Assumed: n1
|
|
Assumed: n2
|
|
Set: lean::pp::implicit
|
|
@f N n1 n2
|
|
@f ((N → N) → N → N) (λ x : N → N, x) (λ y : N → N, y)
|
|
Assumed: EqNice
|
|
@EqNice N n1 n2
|
|
@f N n1 n2 : N
|
|
@Congr : Π (A : (Type U)) (B : A → (Type U)) (f g : Π x : A, B x) (a b : A), f == g → a == b → f a == g b
|
|
@f N n1 n2
|
|
Assumed: a
|
|
Assumed: b
|
|
Assumed: c
|
|
Assumed: g
|
|
Assumed: H1
|
|
Proved: Pr
|
|
Axiom H1 : @eq N a b ∧ @eq N b c
|
|
Theorem Pr : @eq N (g a) (g c) :=
|
|
@Congr N
|
|
(λ x : N, N)
|
|
g
|
|
g
|
|
a
|
|
c
|
|
(@Refl (N → N) g)
|
|
(@Trans N a b c (@Conjunct1 (@eq N a b) (@eq N b c) H1) (@Conjunct2 (@eq N a b) (@eq N b c) H1))
|