mirror of https://github.com/nmvdw/HITs-Examples
Simplified proof of Bfin => Kfin
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FiniteSets/subobjects
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@ -359,16 +359,8 @@ Section bfin_kfin.
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- apply Kf_unfold.
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exists ∅. intros [].
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- intros B [n f] IH.
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strip_truncations.
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apply Kf_unfold in IH.
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destruct IH as [X HX].
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apply Kf_unfold.
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exists ((fmap FSet inl X) ∪ {|inr tt|}); simpl.
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intros [a | []]; apply tr.
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+ left.
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apply fmap_isIn.
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apply (HX a).
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+ right. apply (tr idpath).
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apply Kf_sum ; try assumption.
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apply Kf_Unit.
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Defined.
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Definition bfin_to_kfin_sub A : forall (P : Sub A), Bfin P -> Kf_sub _ P.
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