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Uses merely decidable equality, added length.

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Niels van der Weide
2017-09-21 14:12:51 +02:00
parent 0def5869cd
commit 39e2ce1c05
15 changed files with 193 additions and 106 deletions
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4
FiniteSets/subobjects/enumerated.v
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@@ -254,15 +254,13 @@ Section fset_dec_enumerated.
forall (X : FSet A),
hexists (fun (ls : list A) => forall a, a ∈ X = listExt ls a).
Proof.
simple refine (FSet_cons_ind _ _ _ _ _ _); simpl.
simple refine (FSet_cons_ind _ _ _ _ _ _) ; try (intros ; apply path_ishprop).
- apply tr. exists nil. simpl. done.
- intros a X Hls.
strip_truncations. apply tr.
destruct Hls as [ls Hls].
exists (cons a ls). intros b. cbn.
apply (ap (fun z => _ ∨ z) (Hls b)).
- intros. apply path_ishprop.
- intros. apply path_ishprop.
Defined.
Definition Kf_enumerated : Kf A -> enumerated A.