27 lines
1.1 KiB
Text
27 lines
1.1 KiB
Text
import cast
|
|
set::option pp::colors false
|
|
|
|
check fun (A A': TypeM)
|
|
(B : A -> TypeM)
|
|
(B' : A' -> TypeM)
|
|
(f : Pi x : A, B x)
|
|
(g : Pi x : A', B' x)
|
|
(a : A)
|
|
(b : A')
|
|
(H1 : (Pi x : A, B x) == (Pi x : A', B' x))
|
|
(H2 : f == g)
|
|
(H3 : a == b),
|
|
let
|
|
S1 : (Pi x : A', B' x) == (Pi x : A, B x) := symm H1,
|
|
L2 : A' == A := dominj S1,
|
|
b' : A := cast L2 b,
|
|
L3 : b == b' := cast::eq L2 b,
|
|
L4 : a == b' := htrans H3 L3,
|
|
L5 : f a == f b' := congr2 f L4,
|
|
g' : (Pi x : A, B x) := cast S1 g,
|
|
L6 : g == g' := cast::eq S1 g,
|
|
L7 : f == g' := htrans H2 L6,
|
|
L8 : f b' == g' b' := congr1 b' L7,
|
|
L9 : f a == g' b' := htrans L5 L8,
|
|
L10 : g' b' == g b := cast::app S1 L2 g b
|
|
in htrans L9 L10
|