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Diffstat (limited to 'test-suite/bugs/closed/3895.v')
| -rw-r--r-- | test-suite/bugs/closed/3895.v | 22 |
1 files changed, 22 insertions, 0 deletions
diff --git a/test-suite/bugs/closed/3895.v b/test-suite/bugs/closed/3895.v new file mode 100644 index 00000000..8659ca2c --- /dev/null +++ b/test-suite/bugs/closed/3895.v @@ -0,0 +1,22 @@ +Notation pr1 := (@projT1 _ _). +Notation compose := (fun g' f' x => g' (f' x)). +Notation "g 'o' f" := (compose g f) (at level 40, left associativity) : +function_scope. +Open Scope function_scope. +Definition ap {A B:Type} (f:A -> B) {x y:A} (p:x = y) : f x = f y := match p +with eq_refl => eq_refl end. +Definition pointwise_paths {A} {P:A->Type} (f g:forall x:A, P x) := forall x:A, +f x = g x. +Notation "f == g" := (pointwise_paths f g) (at level 70, no associativity) : +type_scope. +Theorem Univalence_implies_FunextNondep (A B : Type) +: forall f g : A -> B, f == g -> f = g. +Proof. + intros f g p. + pose (d := fun x : A => existT (fun xy => fst xy = snd xy) (f x, f x) +(eq_refl (f x))). + pose (e := fun x : A => existT (fun xy => fst xy = snd xy) (f x, g x) (p x)). + change f with ((snd o pr1) o d). + change g with ((snd o pr1) o e). + apply (ap (fun g => snd o pr1 o g)). +(* Used to raise a not Found due to a "typo" in solve_evar_evar *) |