diff options
Diffstat (limited to 'test-suite/bugs/closed/3566.v')
| -rw-r--r-- | test-suite/bugs/closed/3566.v | 22 |
1 files changed, 22 insertions, 0 deletions
diff --git a/test-suite/bugs/closed/3566.v b/test-suite/bugs/closed/3566.v new file mode 100644 index 00000000..b2aa8c3c --- /dev/null +++ b/test-suite/bugs/closed/3566.v @@ -0,0 +1,22 @@ +Notation idmap := (fun x => x). +Inductive paths {A : Type} (a : A) : A -> Type := idpath : paths a a. +Arguments idpath {A a} , [A] a. +Notation "x = y :> A" := (@paths A x y) : type_scope. +Notation "x = y" := (x = y :>_) : type_scope. +Delimit Scope path_scope with path. +Definition concat {A : Type} {x y z : A} (p : x = y) (q : y = z) : x = z := match p, q with idpath, idpath => idpath end. +Definition inverse {A : Type} {x y : A} (p : x = y) : y = x := match p with idpath => idpath end. +Notation "p @ q" := (concat p q) (at level 20) : path_scope. +Notation "p ^" := (inverse p) (at level 3, format "p '^'") : path_scope. +Class IsEquiv {A B : Type} (f : A -> B) := {}. +Axiom path_universe : forall {A B : Type} (f : A -> B) {feq : IsEquiv f}, (A = B). + +Definition Lift : Type@{i} -> Type@{j} + := Eval hnf in let lt := Type@{i} : Type@{j} in fun T => T. + +Definition lift {T} : T -> Lift T := fun x => x. + +Goal forall x y : Type, x = y. + intros. + pose proof ((fun H0 : idmap _ => (@path_universe _ _ (@lift x) (H0 x) @ + (@path_universe _ _ (@lift x) (H0 x))^)))%path as H''. |