diff options
| -rw-r--r-- | theories/Classes/CMorphisms.v | 2 | ||||
| -rw-r--r-- | theories/Classes/Morphisms.v | 2 | ||||
| -rw-r--r-- | theories/Classes/Morphisms_Prop.v | 2 | ||||
| -rw-r--r-- | theories/FSets/FMapAVL.v | 2 | ||||
| -rw-r--r-- | theories/FSets/FMapFacts.v | 94 | ||||
| -rw-r--r-- | theories/FSets/FMapPositive.v | 4 | ||||
| -rw-r--r-- | theories/FSets/FSetCompat.v | 10 | ||||
| -rw-r--r-- | theories/FSets/FSetEqProperties.v | 2 | ||||
| -rw-r--r-- | theories/FSets/FSetProperties.v | 44 |
9 files changed, 87 insertions, 75 deletions
diff --git a/theories/Classes/CMorphisms.v b/theories/Classes/CMorphisms.v index c247bc11dc..598bd8b9c5 100644 --- a/theories/Classes/CMorphisms.v +++ b/theories/Classes/CMorphisms.v @@ -638,7 +638,7 @@ Instance PartialOrder_proper_type `(PartialOrder A eqA R) : Proper (eqA==>eqA==>iffT) R. Proof. intros. -apply proper_sym_arrow_iffT_2; auto with *. +apply proper_sym_arrow_iffT_2. 1-2: auto with crelations. intros x x' Hx y y' Hy Hr. transitivity x. - generalize (partial_order_equivalence x x'); compute; intuition. diff --git a/theories/Classes/Morphisms.v b/theories/Classes/Morphisms.v index 5adb927357..43adb0b69f 100644 --- a/theories/Classes/Morphisms.v +++ b/theories/Classes/Morphisms.v @@ -640,7 +640,7 @@ Instance PartialOrder_proper `(PartialOrder A eqA R) : Proper (eqA==>eqA==>iff) R. Proof. intros. -apply proper_sym_impl_iff_2; auto with *. +apply proper_sym_impl_iff_2. 1-2: auto with relations. intros x x' Hx y y' Hy Hr. transitivity x. - generalize (partial_order_equivalence x x'); compute; intuition. diff --git a/theories/Classes/Morphisms_Prop.v b/theories/Classes/Morphisms_Prop.v index 418f7a8767..7d0382ec43 100644 --- a/theories/Classes/Morphisms_Prop.v +++ b/theories/Classes/Morphisms_Prop.v @@ -75,7 +75,7 @@ Instance Acc_pt_morphism {A:Type}(E R : A->A->Prop) `(Equivalence _ E) `(Proper _ (E==>E==>iff) R) : Proper (E==>iff) (Acc R). Proof. - apply proper_sym_impl_iff; auto with *. + apply proper_sym_impl_iff. auto with relations. intros x y EQ WF. apply Acc_intro; intros z Hz. rewrite <- EQ in Hz. now apply Acc_inv with x. Qed. diff --git a/theories/FSets/FMapAVL.v b/theories/FSets/FMapAVL.v index 8cdc6e54c5..82055c4752 100644 --- a/theories/FSets/FMapAVL.v +++ b/theories/FSets/FMapAVL.v @@ -1335,7 +1335,7 @@ Proof. apply Hl; auto. constructor. apply Hr; eauto. - apply InA_InfA with (eqA:=eqke); auto with *. intros (y',e') H6. + apply InA_InfA with (eqA:=eqke). auto with typeclass_instances. intros (y',e') H6. destruct (elements_aux_mapsto r acc y' e'); intuition. red; simpl; eauto. red; simpl; eauto with ordered_type. diff --git a/theories/FSets/FMapFacts.v b/theories/FSets/FMapFacts.v index 1eb6a3f372..2001201ec3 100644 --- a/theories/FSets/FMapFacts.v +++ b/theories/FSets/FMapFacts.v @@ -760,7 +760,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E). Instance eqke_equiv : Equivalence eqke. Proof. unfold eq_key_elt; split; repeat red; firstorder. - eauto with *. + eauto. congruence. Qed. @@ -910,9 +910,9 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E). assert (Hstep' : forall k e a m' m'', InA eqke (k,e) l -> ~In k m' -> Add k e m' m'' -> P m' a -> P m'' (F (k,e) a)). intros k e a m' m'' H ? ? ?; eapply Hstep; eauto. - revert H; unfold l; rewrite InA_rev, elements_mapsto_iff; auto with *. + revert H; unfold l; rewrite InA_rev, elements_mapsto_iff. auto. assert (Hdup : NoDupA eqk l). - unfold l. apply NoDupA_rev; try red; unfold eq_key ; eauto with *. + unfold l. apply NoDupA_rev; try red; unfold eq_key. auto with typeclass_instances. apply elements_3w. assert (Hsame : forall k, find k m = findA (eqb k) l). intros k. unfold l. rewrite elements_o, findA_rev; auto. @@ -993,7 +993,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E). rewrite 2 fold_spec_right. set (l:=rev (elements m)). assert (Rstep' : forall k e a b, InA eqke (k,e) l -> R a b -> R (f k e a) (g k e b)) by - (intros; apply Rstep; auto; rewrite elements_mapsto_iff, <- InA_rev; auto with *). + (intros; apply Rstep; auto; rewrite elements_mapsto_iff, <- InA_rev; assumption). clearbody l; clear Rstep m. induction l; simpl; auto. apply Rstep'; auto. @@ -1107,17 +1107,20 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E). Proof. intros. rewrite 2 fold_spec_right. - assert (NoDupA eqk (rev (elements m1))) by (auto with *). - assert (NoDupA eqk (rev (elements m2))) by (auto with *). - apply fold_right_equivlistA_restr with (R:=complement eqk)(eqA:=eqke); - auto with *. + assert (NoDupA eqk (rev (elements m1))) by auto with map typeclass_instances. + assert (NoDupA eqk (rev (elements m2))) by auto with map typeclass_instances. + apply fold_right_equivlistA_restr with (R:=complement eqk)(eqA:=eqke). + auto with typeclass_instances. + auto. + 2: auto with crelations. + 4, 5: auto with map. intros (k1,e1) (k2,e2) (Hk,He) a1 a2 Ha; simpl in *; apply Comp; auto. unfold complement, eq_key, eq_key_elt; repeat red. intuition eauto. intros (k,e) (k',e'); unfold eq_key, uncurry; simpl; auto. rewrite <- NoDupA_altdef; auto. intros (k,e). - rewrite 2 InA_rev, <- 2 elements_mapsto_iff, 2 find_mapsto_iff, H; - auto with *. + rewrite 2 InA_rev, <- 2 elements_mapsto_iff, 2 find_mapsto_iff, H. + auto with crelations. Qed. Lemma fold_Equal2 : forall m1 m2 i j, Equal m1 m2 -> eqA i j -> @@ -1125,10 +1128,13 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E). Proof. intros. rewrite 2 fold_spec_right. - assert (NoDupA eqk (rev (elements m1))) by (auto with * ). - assert (NoDupA eqk (rev (elements m2))) by (auto with * ). - apply fold_right_equivlistA_restr2 with (R:=complement eqk)(eqA:=eqke) - ; auto with *. + assert (NoDupA eqk (rev (elements m1))) by auto with map typeclass_instances. + assert (NoDupA eqk (rev (elements m2))) by auto with map typeclass_instances. + apply fold_right_equivlistA_restr2 with (R:=complement eqk)(eqA:=eqke). + auto with typeclass_instances. + 1, 10: auto. + 2: auto with crelations. + 4, 5: auto with map. - intros (k1,e1) (k2,e2) (Hk,He) a1 a2 Ha; simpl in *; apply Comp; auto. - unfold complement, eq_key, eq_key_elt; repeat red. intuition eauto. - intros (k,e) (k',e') z z' h h'; unfold eq_key, uncurry;simpl; auto. @@ -1136,8 +1142,8 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E). auto. - rewrite <- NoDupA_altdef; auto. - intros (k,e). - rewrite 2 InA_rev, <- 2 elements_mapsto_iff, 2 find_mapsto_iff, H; - auto with *. + rewrite 2 InA_rev, <- 2 elements_mapsto_iff, 2 find_mapsto_iff, H. + auto with crelations. Qed. @@ -1149,18 +1155,22 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E). set (f':=uncurry f). change (f k e (fold_right f' i (rev (elements m1)))) with (f' (k,e) (fold_right f' i (rev (elements m1)))). - assert (NoDupA eqk (rev (elements m1))) by (auto with *). - assert (NoDupA eqk (rev (elements m2))) by (auto with *). + assert (NoDupA eqk (rev (elements m1))) by auto with map typeclass_instances. + assert (NoDupA eqk (rev (elements m2))) by auto with map typeclass_instances. apply fold_right_add_restr with - (R:=complement eqk)(eqA:=eqke)(eqB:=eqA); auto with *. + (R:=complement eqk)(eqA:=eqke)(eqB:=eqA). + auto with typeclass_instances. + auto. + 2: auto with crelations. + 4, 5: auto with map. intros (k1,e1) (k2,e2) (Hk,He) a a' Ha; unfold f'; simpl in *. apply Comp; auto. unfold complement, eq_key_elt, eq_key; repeat red; intuition eauto. unfold f'; intros (k1,e1) (k2,e2); unfold eq_key, uncurry; simpl; auto. rewrite <- NoDupA_altdef; auto. - rewrite InA_rev, <- elements_mapsto_iff by (auto with *). firstorder. + rewrite InA_rev, <- elements_mapsto_iff. firstorder. intros (a,b). rewrite InA_cons, 2 InA_rev, <- 2 elements_mapsto_iff, - 2 find_mapsto_iff by (auto with *). + 2 find_mapsto_iff. unfold eq_key_elt; simpl. rewrite H0. rewrite add_o. @@ -1791,7 +1801,7 @@ Module OrdProperties (M:S). Lemma sort_equivlistA_eqlistA : forall l l' : list (key*elt), sort ltk l -> sort ltk l' -> equivlistA eqke l l' -> eqlistA eqke l l'. Proof. - apply SortA_equivlistA_eqlistA; eauto with *. + apply SortA_equivlistA_eqlistA; auto with typeclass_instances. Qed. Ltac clean_eauto := unfold O.eqke, O.ltk; simpl; intuition; eauto. @@ -1842,7 +1852,9 @@ Module OrdProperties (M:S). elements m = elements_lt p m ++ elements_ge p m. Proof. unfold elements_lt, elements_ge, leb; intros. - apply filter_split with (eqA:=eqk) (ltA:=ltk); eauto with *. + apply filter_split with (eqA:=eqk) (ltA:=ltk). + 1-3: auto with typeclass_instances. + 2: auto with map. intros; destruct x; destruct y; destruct p. rewrite gtb_1 in H; unfold O.ltk in H; simpl in *. assert (~ltk (t1,e0) (k,e1)). @@ -1856,14 +1868,14 @@ Module OrdProperties (M:S). (elements_lt (x,e) m ++ (x,e):: elements_ge (x,e) m). Proof. intros; unfold elements_lt, elements_ge. - apply sort_equivlistA_eqlistA; auto with *. - apply (@SortA_app _ eqke); auto with *. - apply (@filter_sort _ eqke); auto with *; clean_eauto. + apply sort_equivlistA_eqlistA. auto with map. + apply (@SortA_app _ eqke). auto with typeclass_instances. + apply (@filter_sort _ eqke). 1-3: auto with typeclass_instances. auto with map. constructor; auto with map. - apply (@filter_sort _ eqke); auto with *; clean_eauto. - rewrite (@InfA_alt _ eqke); auto with *; try (clean_eauto; fail). + apply (@filter_sort _ eqke). 1-3: auto with typeclass_instances. auto with map. + rewrite (@InfA_alt _ eqke). 2-4: auto with typeclass_instances. intros. - rewrite filter_InA in H1; auto with *; destruct H1. + rewrite filter_InA in H1 by auto with map. destruct H1. rewrite leb_1 in H2. destruct y; unfold O.ltk in *; simpl in *. rewrite <- elements_mapsto_iff in H1. @@ -1871,22 +1883,22 @@ Module OrdProperties (M:S). contradict H. exists e0; apply MapsTo_1 with t0; auto with ordered_type. ME.order. - apply (@filter_sort _ eqke); auto with *; clean_eauto. + apply (@filter_sort _ eqke). 1-3: auto with typeclass_instances. auto with map. intros. - rewrite filter_InA in H1; auto with *; destruct H1. + rewrite filter_InA in H1 by auto with map. destruct H1. rewrite gtb_1 in H3. destruct y; destruct x0; unfold O.ltk in *; simpl in *. inversion_clear H2. red in H4; simpl in *; destruct H4. ME.order. - rewrite filter_InA in H4; auto with *; destruct H4. + rewrite filter_InA in H4 by auto with map. destruct H4. rewrite leb_1 in H4. unfold O.ltk in *; simpl in *; ME.order. red; intros a; destruct a. rewrite InA_app_iff, InA_cons, 2 filter_InA, <-2 elements_mapsto_iff, leb_1, gtb_1, find_mapsto_iff, (H0 t0), <- find_mapsto_iff, - add_mapsto_iff by (auto with *). + add_mapsto_iff by auto with map. unfold O.eqke, O.ltk; simpl. destruct (E.compare t0 x); intuition; try fold (~E.eq x t0); auto with ordered_type. - elim H; exists e0; apply MapsTo_1 with t0; auto. @@ -1898,8 +1910,8 @@ Module OrdProperties (M:S). eqlistA eqke (elements m') (elements m ++ (x,e)::nil). Proof. intros. - apply sort_equivlistA_eqlistA; auto with *. - apply (@SortA_app _ eqke); auto with *. + apply sort_equivlistA_eqlistA. auto with map. + apply (@SortA_app _ eqke). auto with typeclass_instances. auto with map. auto. intros. inversion_clear H2. destruct x0; destruct y. @@ -1911,7 +1923,7 @@ Module OrdProperties (M:S). red; intros a; destruct a. rewrite InA_app_iff, InA_cons, InA_nil, <- 2 elements_mapsto_iff, find_mapsto_iff, (H0 t0), <- find_mapsto_iff, - add_mapsto_iff by (auto with *). + add_mapsto_iff. unfold O.eqke; simpl. intuition. destruct (E.eq_dec x t0) as [Heq|Hneq]; auto. exfalso. @@ -1926,9 +1938,9 @@ Module OrdProperties (M:S). eqlistA eqke (elements m') ((x,e)::elements m). Proof. intros. - apply sort_equivlistA_eqlistA; auto with *. + apply sort_equivlistA_eqlistA. auto with map. change (sort ltk (((x,e)::nil) ++ elements m)). - apply (@SortA_app _ eqke); auto with *. + apply (@SortA_app _ eqke). auto with typeclass_instances. auto. auto with map. intros. inversion_clear H1. destruct y; destruct x0. @@ -1940,7 +1952,7 @@ Module OrdProperties (M:S). red; intros a; destruct a. rewrite InA_cons, <- 2 elements_mapsto_iff, find_mapsto_iff, (H0 t0), <- find_mapsto_iff, - add_mapsto_iff by (auto with *). + add_mapsto_iff. unfold O.eqke; simpl. intuition. destruct (E.eq_dec x t0) as [Heq|Hneq]; auto. exfalso. @@ -1954,7 +1966,7 @@ Module OrdProperties (M:S). Equal m m' -> eqlistA eqke (elements m) (elements m'). Proof. intros. - apply sort_equivlistA_eqlistA; auto with *. + apply sort_equivlistA_eqlistA. 1-2: auto with map. red; intros. destruct x; do 2 rewrite <- elements_mapsto_iff. do 2 rewrite find_mapsto_iff; rewrite H; split; auto. @@ -2056,7 +2068,7 @@ Module OrdProperties (M:S). inversion_clear H1 as [? ? H2|? ? H2]. red in H2; destruct H2; simpl in *; ME.order. inversion_clear H4. rename H1 into H3. - rewrite (@InfA_alt _ eqke) in H3; eauto with *. + rewrite (@InfA_alt _ eqke) in H3 by auto with typeclass_instances. apply (H3 (y,x0)); auto. Qed. diff --git a/theories/FSets/FMapPositive.v b/theories/FSets/FMapPositive.v index e9cb0a6aa7..c3c6c96997 100644 --- a/theories/FSets/FMapPositive.v +++ b/theories/FSets/FMapPositive.v @@ -679,7 +679,7 @@ Module PositiveMap <: S with Module E:=PositiveOrderedTypeBits. simpl; auto. destruct o; simpl; intros. (* Some *) - apply (SortA_app (eqA:=eq_key_elt)); auto with *. + apply (SortA_app (eqA:=eq_key_elt)). 1-2: auto with typeclass_instances. constructor; auto. apply In_InfA; intros. destruct y0. @@ -698,7 +698,7 @@ Module PositiveMap <: S with Module E:=PositiveOrderedTypeBits. eapply xelements_bits_lt_1; eauto. eapply xelements_bits_lt_2; eauto. (* None *) - apply (SortA_app (eqA:=eq_key_elt)); auto with *. + apply (SortA_app (eqA:=eq_key_elt)). auto with typeclass_instances. 1-2: auto. intros x0 y0. do 2 rewrite InA_alt. intros (y1,(Hy1,H)) (y2,(Hy2,H0)). diff --git a/theories/FSets/FSetCompat.v b/theories/FSets/FSetCompat.v index 4edeaee72e..bff999042b 100644 --- a/theories/FSets/FSetCompat.v +++ b/theories/FSets/FSetCompat.v @@ -381,22 +381,22 @@ Module Update_Sets Instance lt_strorder : StrictOrder lt. Proof. split. - intros x Hx. apply (M.lt_not_eq Hx); auto with *. + intros x Hx. apply (M.lt_not_eq Hx). auto with crelations. exact M.lt_trans. Qed. Instance lt_compat : Proper (eq==>eq==>iff) lt. Proof. - apply proper_sym_impl_iff_2; auto with *. + apply proper_sym_impl_iff_2. 1-2: auto with crelations. intros s s' Hs u u' Hu H. assert (H0 : lt s' u). destruct (M.compare s' u) as [H'|H'|H']; auto. - elim (M.lt_not_eq H). transitivity s'; auto with *. + elim (M.lt_not_eq H). transitivity s'; auto. elim (M.lt_not_eq (M.lt_trans H H')); auto. destruct (M.compare s' u') as [H'|H'|H']; auto. elim (M.lt_not_eq H). - transitivity u'; auto with *. transitivity s'; auto with *. - elim (M.lt_not_eq (M.lt_trans H' H0)); auto with *. + transitivity u'. 2: auto with crelations. transitivity s'; auto. + elim (M.lt_not_eq (M.lt_trans H' H0)); auto with crelations. Qed. Definition compare s s' := diff --git a/theories/FSets/FSetEqProperties.v b/theories/FSets/FSetEqProperties.v index 1542660ab7..ac08351ad9 100644 --- a/theories/FSets/FSetEqProperties.v +++ b/theories/FSets/FSetEqProperties.v @@ -924,7 +924,7 @@ transitivity (f x (fold f s0 i)). apply fold_add with (eqA:=eqA); auto with set. transitivity (g x (fold f s0 i)); auto with set. transitivity (g x (fold g s0 i)); auto with set. -apply gc; auto with *. +apply gc; auto with set. symmetry; apply fold_add with (eqA:=eqA); auto. do 2 rewrite fold_empty; reflexivity. Qed. diff --git a/theories/FSets/FSetProperties.v b/theories/FSets/FSetProperties.v index 88d12fc387..98b445580b 100644 --- a/theories/FSets/FSetProperties.v +++ b/theories/FSets/FSetProperties.v @@ -365,7 +365,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E). assert (Pstep' : forall x a s' s'', InA x l -> ~In x s' -> Add x s' s'' -> P s' a -> P s'' (f x a)). intros; eapply Pstep; eauto. - rewrite elements_iff, <- InA_rev; auto with *. + rewrite elements_iff, <- InA_rev; auto. assert (Hdup : NoDup l) by (unfold l; eauto using elements_3w, NoDupA_rev with *). assert (Hsame : forall x, In x s <-> InA x l) by @@ -435,7 +435,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E). intros A B R f g i j s Rempty Rstep. rewrite 2 fold_spec_right. set (l:=rev (elements s)). assert (Rstep' : forall x a b, InA x l -> R a b -> R (f x a) (g x b)) by - (intros; apply Rstep; auto; rewrite elements_iff, <- InA_rev; auto with *). + (intros; apply Rstep; auto; rewrite elements_iff, <- InA_rev; auto). clearbody l; clear Rstep s. induction l; simpl; auto. Qed. @@ -487,7 +487,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E). fold f s i = fold_right f i l. Proof. intros; exists (rev (elements s)); split. - apply NoDupA_rev; auto with *. + apply NoDupA_rev. auto with typeclass_instances. auto with set. split; intros. rewrite elements_iff; do 2 rewrite InA_alt. split; destruct 1; generalize (In_rev (elements s) x0); exists x0; intuition. @@ -521,7 +521,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E). intros; destruct (fold_0 s i f) as (l,(Hl, (Hl1, Hl2))); destruct (fold_0 s' i f) as (l',(Hl', (Hl'1, Hl'2))). rewrite Hl2; rewrite Hl'2; clear Hl2 Hl'2. - apply fold_right_add with (eqA:=E.eq)(eqB:=eqA); auto with *. + apply fold_right_add with (eqA:=E.eq)(eqB:=eqA). auto with typeclass_instances. 1-5: auto. rewrite <- Hl1; auto. intros a; rewrite InA_cons; rewrite <- Hl1; rewrite <- Hl'1; rewrite (H2 a); intuition. @@ -550,7 +550,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E). intros. apply fold_rel with (R:=fun u v => eqA u (f x v)); intros. reflexivity. - transitivity (f x0 (f x b)); auto. apply Comp; auto with *. + transitivity (f x0 (f x b)); auto. apply Comp; auto. Qed. (** ** Fold is a morphism *) @@ -559,7 +559,7 @@ Module WProperties_fun (Import E : DecidableType)(M : WSfun E). eqA (fold f s i) (fold f s i'). Proof. intros. apply fold_rel with (R:=eqA); auto. - intros; apply Comp; auto with *. + intros; apply Comp; auto. Qed. Lemma fold_equal : @@ -914,7 +914,7 @@ Module OrdProperties (M:S). Lemma sort_equivlistA_eqlistA : forall l l' : list elt, sort E.lt l -> sort E.lt l' -> equivlistA E.eq l l' -> eqlistA E.eq l l'. Proof. - apply SortA_equivlistA_eqlistA; eauto with *. + apply SortA_equivlistA_eqlistA; auto with typeclass_instances. Qed. Definition gtb x y := match E.compare x y with GT _ => true | _ => false end. @@ -958,7 +958,7 @@ Module OrdProperties (M:S). elements s = elements_lt x s ++ elements_ge x s. Proof. unfold elements_lt, elements_ge, leb; intros. - eapply (@filter_split _ E.eq _ E.lt); auto with *. + eapply (@filter_split _ E.eq _ E.lt). 1-2: auto with typeclass_instances. 2: auto with set. intros. rewrite gtb_1 in H. assert (~E.lt y x). @@ -972,32 +972,32 @@ Module OrdProperties (M:S). Proof. intros; unfold elements_ge, elements_lt. apply sort_equivlistA_eqlistA; auto with set. - apply (@SortA_app _ E.eq); auto with *. - apply (@filter_sort _ E.eq); auto with *. + apply (@SortA_app _ E.eq). auto with typeclass_instances. + apply (@filter_sort _ E.eq). 1-3: auto with typeclass_instances. auto with set. constructor; auto. - apply (@filter_sort _ E.eq); auto with *. - rewrite ME.Inf_alt by (apply (@filter_sort _ E.eq); eauto with *). + apply (@filter_sort _ E.eq). 1-3: auto with typeclass_instances. auto with set. + rewrite ME.Inf_alt by (apply (@filter_sort _ E.eq); auto with set typeclass_instances). intros. - rewrite filter_InA in H1; auto with *; destruct H1. + rewrite filter_InA in H1 by auto with fset. destruct H1. rewrite leb_1 in H2. rewrite <- elements_iff in H1. assert (~E.eq x y). contradict H; rewrite H; auto. ME.order. intros. - rewrite filter_InA in H1; auto with *; destruct H1. + rewrite filter_InA in H1 by auto with fset. destruct H1. rewrite gtb_1 in H3. inversion_clear H2. ME.order. - rewrite filter_InA in H4; auto with *; destruct H4. + rewrite filter_InA in H4 by auto with fset. destruct H4. rewrite leb_1 in H4. ME.order. red; intros a. rewrite InA_app_iff, InA_cons, !filter_InA, <-elements_iff, - leb_1, gtb_1, (H0 a) by auto with *. + leb_1, gtb_1, (H0 a) by auto with fset. intuition. destruct (E.compare a x); intuition. - fold (~E.lt a x); auto with *. + fold (~E.lt a x); auto with ordered_type set. Qed. Definition Above x s := forall y, In y s -> E.lt y x. @@ -1008,15 +1008,15 @@ Module OrdProperties (M:S). eqlistA E.eq (elements s') (elements s ++ x::nil). Proof. intros. - apply sort_equivlistA_eqlistA; auto with *. - apply (@SortA_app _ E.eq); auto with *. + apply sort_equivlistA_eqlistA. auto with set. + apply (@SortA_app _ E.eq). auto with typeclass_instances. auto with set. auto. intros. inversion_clear H2. rewrite <- elements_iff in H1. apply ME.lt_eq with x; auto with ordered_type. inversion H3. red; intros a. - rewrite InA_app_iff, InA_cons, InA_nil by auto with *. + rewrite InA_app_iff, InA_cons, InA_nil. do 2 rewrite <- elements_iff; rewrite (H0 a); intuition. Qed. @@ -1025,9 +1025,9 @@ Module OrdProperties (M:S). eqlistA E.eq (elements s') (x::elements s). Proof. intros. - apply sort_equivlistA_eqlistA; auto with *. + apply sort_equivlistA_eqlistA. auto with set. change (sort E.lt ((x::nil) ++ elements s)). - apply (@SortA_app _ E.eq); auto with *. + apply (@SortA_app _ E.eq). auto with typeclass_instances. auto. auto with set. intros. inversion_clear H1. rewrite <- elements_iff in H2. |