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(* This used to fail in Coq version 8.1 beta due to a non variable
universe (issued by template polymorphism) being sent by
pretyping to the kernel (bug #1182) *)
Variable T : Type.
Variable x : nat*nat.
Check let (_, _) := x in sigT (fun _ : T => nat).
(* This used to raise an anomaly in V8.4, up to pl2 *)
Goal {x: nat & x=x}.
Fail exists (fun x =>
match
projT2 (projT2 x) as e in (_ = y)
return _ = existT _ (projT1 x) (existT _ y e)
with
| eq_refl => eq_refl
end).
Abort.
(* Some tests with ltac matching on building "if" and "let" *)
Goal forall b c d, (if negb b then c else d) = 0.
intros.
match goal with
|- (if ?b then ?c else ?d) = 0 => transitivity (if b then d else c)
end.
Abort.
Definition swap {A} {B} '((x,y):A*B) := (y,x).
Goal forall p, (let '(x,y) := swap p in x + y) = 0.
intros.
match goal with
|- (let '(x,y) := ?p in x + y) = 0 => transitivity (let (x,y) := p in x+y)
end.
Abort.
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