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(* Bug #2137
The fsetdec tactic is sensitive to which way round the arguments to <> are.
In the small, self-contained example below, it is able to solve the goal
if it knows that "b <> a", but not if it knows that "a <> b". I would expect
it to be able to solve hte goal in either case.
I have coq r12238.
Thanks
Ian
*)
Require Import Arith FSets 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 ( s0 : NatSet.t )
( a b : nat ),
b <> a
-> ~(NatSet.In a s0)
-> ~(NatSet.In a (NatSet.add b s0)).
Proof.
intros.
fsetdec.
Qed.
Lemma ThisLemmaWasFailing : forall ( s0 : NatSet.t )
( a b : nat ),
a <> b
-> ~(NatSet.In a s0)
-> ~(NatSet.In a (NatSet.add b s0)).
Proof.
intros.
fsetdec.
(*
Error: Tactic failure: because the goal is beyond the scope of this tactic.
*)
Qed.
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