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Simplified proof of Bfin => Kfin

This commit is contained in:
Niels van der Weide 2017-10-03 21:34:23 +02:00
parent fffdb87b4f
commit 764b0147fe
1 changed files with 2 additions and 10 deletions
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12
FiniteSets/subobjects/b_finite.v
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@ -359,16 +359,8 @@ Section bfin_kfin.
- apply Kf_unfold. - apply Kf_unfold.
exists ∅. intros []. exists ∅. intros [].
- intros B [n f] IH. - intros B [n f] IH.
strip_truncations. apply Kf_sum ; try assumption.
apply Kf_unfold in IH. apply Kf_Unit.
destruct IH as [X HX].
apply Kf_unfold.
exists ((fmap FSet inl X) ∪ {|inr tt|}); simpl.
intros [a | []]; apply tr.
+ left.
apply fmap_isIn.
apply (HX a).
+ right. apply (tr idpath).
Defined. Defined.
Definition bfin_to_kfin_sub A : forall (P : Sub A), Bfin P -> Kf_sub _ P. Definition bfin_to_kfin_sub A : forall (P : Sub A), Bfin P -> Kf_sub _ P.