36 lines
1 KiB
Text
36 lines
1 KiB
Text
|
|
Variable f {A : Type} (a b : A) : A
|
|
Variable N : Type
|
|
Variable n1 : N
|
|
Variable n2 : N
|
|
Set lean::pp::implicit true
|
|
Show f n1 n2
|
|
Show f (fun x : N -> N, x) (fun y : _, y)
|
|
Variable EqNice {A : Type} (lhs rhs : A) : Bool
|
|
Infix 50 === : EqNice
|
|
Show n1 === n2
|
|
Check f n1 n2
|
|
Check Congr
|
|
Show f n1 n2
|
|
Theorem CongrI {A : Type u} {B : A → Type u} {f g : Π x : A, B x} {a b : A} (H1 : f = g) (H2 : a = b) : (f a) = (g b) :=
|
|
Congr A B f g a b H1 H2
|
|
Theorem TransI {A : Type u} {a b c : A} (H1 : a = b) (H2 : b = c) : a = c :=
|
|
Trans A a b c H1 H2
|
|
Theorem ReflI {A : Type u} (a : A) : a = a :=
|
|
Refl A a
|
|
Theorem SymmI {A : Type u} {a b : A} (H : a = b) : b = a :=
|
|
Symm A a b H
|
|
Theorem Conj1I {a b : Bool} (H : a && b) : a :=
|
|
Conjunct1 a b H
|
|
Theorem Conj2I {a b : Bool} (H : a && b) : b :=
|
|
Conjunct2 a b H
|
|
Variable a : N
|
|
Variable b : N
|
|
Variable c : N
|
|
Variable g : N -> N
|
|
Axiom H1 : a = b && b = c
|
|
Theorem Pr : (g a) = (g c) :=
|
|
CongrI (ReflI g) (TransI (Conj1I H1) (Conj2I H1))
|
|
Show Environment 1
|
|
|
|
|