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Code Issues Releases Wiki Activity

Length also uses merely decidable equality

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Niels van der Weide 2017-09-21 14:17:48 +02:00
parent 39e2ce1c05
commit 7f9b2b7032
1 changed files with 9 additions and 5 deletions
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14
FiniteSets/kuratowski/length.v
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@ -1,8 +1,8 @@
Require Import HoTT HitTactics. Require Import HoTT HitTactics prelude.
Require Import kuratowski.operations kuratowski.properties kuratowski.kuratowski_sets. Require Import kuratowski.operations kuratowski.properties kuratowski.kuratowski_sets.
Section Length. Section Length.
Context {A : Type} `{DecidablePaths A} `{Univalence}. Context {A : Type} `{MerelyDecidablePaths A} `{Univalence}.
Definition length : FSet A -> nat. Definition length : FSet A -> nat.
simple refine (FSet_cons_rec _ _ _ _ _ _). simple refine (FSet_cons_rec _ _ _ _ _ _).
@ -16,11 +16,15 @@ Section Length.
- intros X a b n. - intros X a b n.
simpl. simpl.
simplify_isIn_d. simplify_isIn_d.
destruct (dec (a = b)) as [Hab | Hab]. destruct (m_dec_path a b) as [Hab | Hab].
+ rewrite Hab. simplify_isIn_d. reflexivity. (* destruct (dec (Trunc (-1) (a = b))) as [Hab | Hab]. *)
+ strip_truncations.
rewrite Hab. simplify_isIn_d. reflexivity.
+ rewrite ?singleton_isIn_d_false; auto. + rewrite ?singleton_isIn_d_false; auto.
++ simpl. ++ simpl.
destruct (a ∈_d X), (b ∈_d X) ; reflexivity. destruct (a ∈_d X), (b ∈_d X) ; reflexivity.
++ intro p. contradiction (Hab p^). ++ intro p. contradiction (Hab (tr p^)).
++ intros p.
apply (Hab (tr p)).
Defined. Defined.
End Length. End Length.