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(* Refine and let-in's *)
Goal exists x : nat, x = 0.
refine (let y := 0 + 0 in _).
exists y; auto.
Save test1.
Goal exists x : nat, x = 0.
refine (let y := 0 + 0 in ex_intro _ (y + y) _).
auto.
Save test2.
Goal nat.
refine (let y := 0 in 0 + _).
exact 1.
Save test3.
(* Example submitted by Yves on coqdev *)
Require Import List.
Goal forall l : list nat, l = l.
Proof.
refine
(fun l =>
match l return (l = l) with
| nil => _
| O :: l0 => _
| S _ :: l0 => _
end).
Abort.
(* Submitted by Roland Zumkeller (bug #888) *)
(* The Fix and CoFix rules expect a subgoal even for closed components of the
(co-)fixpoint *)
Goal nat -> nat.
refine (fix f (n : nat) : nat := S _
with pred (n : nat) : nat := n
for f).
exact 0.
Qed.
(* Submitted by Roland Zumkeller (bug #889) *)
(* The types of metas were in metamap and they were not updated when
passing through a binder *)
Goal forall n : nat, nat -> n = 0.
refine
(fun n => fix f (i : nat) : n = 0 := match i with
| O => _
| S _ => _
end).
Abort.
(* Submitted by Roland Zumkeller (bug #931) *)
(* Don't turn dependent evar into metas *)
Goal (forall n : nat, n = 0 -> Prop) -> Prop.
intro P.
refine (P _ _).
reflexivity.
Abort.
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