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(** Bug #2281
In the code below, coq is confused by an equality unless it is first 'subst'ed
away, yet http://coq.inria.fr/stdlib/Coq.FSets.FSetDecide.html says
fsetdec will first perform any necessary zeta and beta reductions and will
invoke subst to eliminate any Coq equalities between finite sets or their
elements.
I have coq r12851.
*)
Require Import Arith.
Require Import FSets.
Require Import FSetWeakList.
Module DecidableNat.
Definition t := nat.
Definition eq := @eq nat.
Definition eq_refl := @refl_equal nat.
Definition eq_sym := @sym_eq nat.
Definition eq_trans := @trans_eq nat.
Definition eq_dec := eq_nat_dec.
End DecidableNat.
Module NatSet := Make(DecidableNat).
Module Export NameSetDec := WDecide (NatSet).
Lemma ThisLemmaWorks : forall ( s1 s2 : NatSet.t )
( H : s1 = s2 ),
NatSet.Equal s1 s2.
Proof.
intros.
subst.
fsetdec.
Qed.
Import FSetDecideAuxiliary.
Lemma ThisLemmaWasFailing : forall ( s1 s2 : NatSet.t )
( H : s1 = s2 ),
NatSet.Equal s1 s2.
Proof.
intros.
fsetdec.
(* Error: Tactic failure: because the goal is beyond the scope of this tactic.
*)
Qed.
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