diff options
author | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-04-15 22:06:11 +0000 |
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committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-04-15 22:06:11 +0000 |
commit | e1f5180e88bf02a22c954ddbdcbdfeb168d264a6 (patch) | |
tree | 86e1f5b98681f5e85aef645a9de894508d98920b /theories/Reals | |
parent | 25c1cfeea010b7267955d6683a381b50e2f52f71 (diff) |
Fixing tauto "special" behavior on singleton types w/ 2 parameters (bug #2680).
- tauto/intuition now works uniformly on and, prod, or, sum, False,
Empty_set, unit, True (and isomorphic copies of them), iff, ->, and
on all inhabited singleton types with a no-arguments constructor
such as "eq t t" (even though the last case goes out of
propositional logic: this features is so often used that it is
difficult to come back on it).
- New dtauto and dintuition works on all inductive types with one
constructors and no real arguments (for instance, they work on
records such as "Equivalence"), in addition to -> and eq-like types.
- Moreover, both of them no longer unfold inner negations (this is a
souce of incompatibility for intuition and evaluation of the level
of incompatibility on contribs still needs to be done).
Incidentally, and amazingly, fixing bug #2680 made that constants
InfA_compat and InfA_eqA in SetoidList.v lost one argument: old tauto
had indeed destructed a section hypothesis "@StrictOrder A ltA@
thinking it was a conjunction, making this section hypothesis
artificially necessary while it was not.
Renouncing to the unfolding of inner negations made auto/eauto
sometimes succeeding more, sometimes succeeding less. There is by the
way a (standard) problem with not in auto/eauto: even when given as an
"unfold hint", it works only in goals, not in hypotheses, so that auto
is not able to solve something like "forall P, (forall x, ~ P x) -> P
0 -> False". Should we automatically add a lemma of type "HYPS -> A ->
False" in the hint database everytime a lemma ""HYPS -> ~A" is
declared (and "unfold not" is a hint), and similarly for all unfold
hints?
At this occasion, also re-did some proofs of Znumtheory.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15180 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals')
-rw-r--r-- | theories/Reals/RIneq.v | 10 | ||||
-rw-r--r-- | theories/Reals/ROrderedType.v | 2 |
2 files changed, 7 insertions, 5 deletions
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index 70f4ff0d9..944e7da21 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -43,7 +43,7 @@ Hint Immediate Rge_refl: rorders. Lemma Rlt_irrefl : forall r, ~ r < r. Proof. - generalize Rlt_asym. intuition eauto. + intros r H; eapply Rlt_asym; eauto. Qed. Hint Resolve Rlt_irrefl: real. @@ -64,7 +64,9 @@ Qed. (**********) Lemma Rlt_dichotomy_converse : forall r1 r2, r1 < r2 \/ r1 > r2 -> r1 <> r2. Proof. - generalize Rlt_not_eq Rgt_not_eq. intuition eauto. + intuition. + - apply Rlt_not_eq in H1. eauto. + - apply Rgt_not_eq in H1. eauto. Qed. Hint Resolve Rlt_dichotomy_converse: real. @@ -74,7 +76,7 @@ Hint Resolve Rlt_dichotomy_converse: real. Lemma Req_dec : forall r1 r2, r1 = r2 \/ r1 <> r2. Proof. intros; generalize (total_order_T r1 r2) Rlt_dichotomy_converse; - intuition eauto 3. + unfold not; intuition eauto 3. Qed. Hint Resolve Req_dec: real. @@ -175,7 +177,7 @@ Proof. eauto using Rnot_gt_ge with rorders. Qed. Lemma Rlt_not_le : forall r1 r2, r2 < r1 -> ~ r1 <= r2. Proof. generalize Rlt_asym Rlt_dichotomy_converse; unfold Rle in |- *. - intuition eauto 3. + unfold not; intuition eauto 3. Qed. Hint Immediate Rlt_not_le: real. diff --git a/theories/Reals/ROrderedType.v b/theories/Reals/ROrderedType.v index 0a8d89c77..eeafbde9b 100644 --- a/theories/Reals/ROrderedType.v +++ b/theories/Reals/ROrderedType.v @@ -15,7 +15,7 @@ Local Open Scope R_scope. Lemma Req_dec : forall r1 r2:R, {r1 = r2} + {r1 <> r2}. Proof. intros; generalize (total_order_T r1 r2) Rlt_dichotomy_converse; - intuition eauto 3. + intuition eauto. Qed. Definition Reqb r1 r2 := if Req_dec r1 r2 then true else false. |