24 lines
987 B
Text
24 lines
987 B
Text
Variable C : Pi (A B : Type) (H : A = B) (a : A), B
|
|
|
|
Variable D : Pi (A A' : Type) (B : A -> Type) (B' : A' -> Type) (H : (Pi x : A, B x) = (Pi x : A', B' x)), A = A'
|
|
|
|
Variable R : Pi (A A' : Type) (B : A -> Type) (B' : A' -> Type) (H : (Pi x : A, B x) = (Pi x : A', B' x)) (a : A),
|
|
(B a) = (B' (C A A' (D A A' B B' H) a))
|
|
|
|
Theorem R2 (A A' B B' : Type) (H : (A -> B) = (A' -> B')) (a : A) : B = B' := R _ _ _ _ H a
|
|
|
|
print Environment 1
|
|
|
|
Theorem R3 : Pi (A1 A2 B1 B2 : Type) (H : (A1 -> B1) = (A2 -> B2)) (a : A1), B1 = B2 :=
|
|
fun (A1 A2 B1 B2 : Type) (H : (A1 -> B1) = (A2 -> B2)) (a : A1),
|
|
R _ _ _ _ H a
|
|
|
|
Theorem R4 : Pi (A1 A2 B1 B2 : Type) (H : (A1 -> B1) = (A2 -> B2)) (a : A1), B1 = B2 :=
|
|
fun (A1 A2 B1 B2 : Type) (H : (A1 -> B1) = (A2 -> B2)) (a : _),
|
|
R _ _ _ _ H a
|
|
|
|
Theorem R5 : Pi (A1 A2 B1 B2 : Type) (H : (A1 -> B1) = (A2 -> B2)) (a : A1), B1 = B2 :=
|
|
fun (A1 A2 B1 B2 : Type) (H : _) (a : _),
|
|
R _ _ _ _ H a
|
|
|
|
print Environment 1
|