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Further simplifications in interface

This commit is contained in:
Niels 2017-08-15 22:05:31 +02:00
parent e29e978218
commit e1bc900abc
1 changed files with 15 additions and 23 deletions
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26
FiniteSets/implementations/interface.v
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@ -33,14 +33,10 @@ Section interface.
* refine (tr({|a|};_)). * refine (tr({|a|};_)).
apply f_singleton. apply f_singleton.
* intros ; apply path_ishprop. * intros ; apply path_ishprop.
- intros Y1 Y2 HY1 HY2. - intros Y1 Y2 [X1' ?] [X2' ?].
destruct HY1 as [X1' HX1].
destruct HY2 as [X2' HX2].
simple refine (BuildContr _ _ _). simple refine (BuildContr _ _ _).
* simple refine (Trunc_rec _ X1') ; intro X1. * simple refine (Trunc_rec _ X1') ; intros [X1 fX1].
simple refine (Trunc_rec _ X2') ; intro X2. simple refine (Trunc_rec _ X2') ; intros [X2 fX2].
destruct X1 as [X1 fX1].
destruct X2 as [X2 fX2].
refine (tr(X1 ∪ X2;_)). refine (tr(X1 ∪ X2;_)).
rewrite f_union, fX1, fX2. rewrite f_union, fX1, fX2.
reflexivity. reflexivity.
@ -97,7 +93,6 @@ Section quotient_surjection.
Proof. Proof.
apply isembedding_isinj_hset. apply isembedding_isinj_hset.
unfold isinj. unfold isinj.
simpl.
hrecursion ; [ | intros; apply path_ishprop ]. hrecursion ; [ | intros; apply path_ishprop ].
intro. intro.
hrecursion ; [ | intros; apply path_ishprop ]. hrecursion ; [ | intros; apply path_ishprop ].
@ -110,16 +105,14 @@ Section quotient_surjection.
apply BuildIsSurjection. apply BuildIsSurjection.
intros Y. intros Y.
destruct (H Y). destruct (H Y).
simple refine (Trunc_rec _ center) ; intro X. simple refine (Trunc_rec _ center) ; intros [a fa].
apply tr. apply (tr(class_of _ a;fa)).
destruct X as [a fa].
apply (class_of _ a;fa).
Defined. Defined.
Definition quotient_iso : quotientB <~> B. Definition quotient_iso : quotientB <~> B.
Proof. Proof.
refine (BuildEquiv _ _ quotientB_to_B _). refine (BuildEquiv _ _ quotientB_to_B _).
apply isequiv_surj_emb; apply _. apply isequiv_surj_emb ; apply _.
Defined. Defined.
Definition reflect_eq : forall (X Y : A), Definition reflect_eq : forall (X Y : A),
@ -210,8 +203,7 @@ Section quotient_properties.
- apply (member a). - apply (member a).
- intros X Y HXY. - intros X Y HXY.
reduce T. reduce T.
rewrite HXY. apply (ap _ HXY).
reflexivity.
Defined. Defined.
Global Instance View_empty A: hasEmpty (View A). Global Instance View_empty A: hasEmpty (View A).
@ -232,7 +224,7 @@ Section quotient_properties.
apply (class_of _ (union a b)). apply (class_of _ (union a b)).
- intros x x' Hxx' y y' Hyy' ; simpl. - intros x x' Hxx' y y' Hyy' ; simpl.
apply related_classes_eq. apply related_classes_eq.
eapply well_defined_union; eauto. eapply well_defined_union ; eauto.
Defined. Defined.
Global Instance View_union A: hasUnion (View A). Global Instance View_union A: hasUnion (View A).
@ -248,7 +240,7 @@ Section quotient_properties.
apply (class_of _ (filter ϕ X)). apply (class_of _ (filter ϕ X)).
- intros X X' HXX' ; simpl. - intros X X' HXX' ; simpl.
apply related_classes_eq. apply related_classes_eq.
eapply well_defined_filter; eauto. eapply well_defined_filter ; eauto.
Defined. Defined.
Hint Unfold Commutative Associative Idempotent NeutralL NeutralR. Hint Unfold Commutative Associative Idempotent NeutralL NeutralR.