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Simplified Kfin=>Bfin

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Niels van der Weide
2017-10-03 21:50:43 +02:00
parent 764b0147fe
commit b638c2592d
1 changed files with 1 additions and 12 deletions
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13
FiniteSets/subobjects/b_finite.v
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@@ -492,21 +492,10 @@ Section kfin_bfin.
simple refine (BuildEquiv _ _ _ _). simple refine (BuildEquiv _ _ _ _).
destruct 1 as [? []]. destruct 1 as [? []].
- intros a. - intros a.
exists 1. apply tr. simpl. apply _.
transitivity Unit; [ | symmetry; apply sum_empty_l ].
unshelve esplit.
+ exact (fun _ => tt).
+ apply isequiv_biinv. split.
* exists (fun _ => (a; tr(idpath))).
intros [b Hb]. strip_truncations.
apply path_sigma' with Hb^.
apply path_ishprop.
* exists (fun _ => (a; tr(idpath))).
intros []. reflexivity.
- intros Y1 Y2 HY1 HY2. - intros Y1 Y2 HY1 HY2.
apply bfin_union; auto. apply bfin_union; auto.
Defined. Defined.
End kfin_bfin. End kfin_bfin.
Instance Kf_to_Bf (X : Type) `{Univalence} `{DecidablePaths X} (Hfin : Kf X) : Finite X. Instance Kf_to_Bf (X : Type) `{Univalence} `{DecidablePaths X} (Hfin : Kf X) : Finite X.