mirror of https://github.com/nmvdw/HITs-Examples
41 lines
1.0 KiB
Coq
41 lines
1.0 KiB
Coq
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(* Operations on [FSet A] when [A] has decidable equality *)
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Require Import HoTT HitTactics.
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Require Export definition operations.
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Section decidable_A.
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Context {A : Type}.
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Context {A_deceq : DecidablePaths A}.
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Context `{Univalence}.
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Global Instance isIn_decidable : forall (a : A) (X : FSet A), Decidable (isIn a X).
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Proof.
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intros a.
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hinduction ; try (intros ; apply path_ishprop).
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- apply _.
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- intros. apply _.
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- intros. apply _.
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Defined.
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Definition isIn_b (a : A) (X : FSet A) :=
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match dec (isIn a X) with
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| inl _ => true
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| inr _ => false
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end.
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Global Instance subset_decidable : forall (X Y : FSet A), Decidable (subset X Y).
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Proof.
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hinduction ; try (intros ; apply path_ishprop).
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- intro ; apply _.
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- intros ; apply _.
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- intros ; apply _.
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Defined.
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Definition subset_b (X Y : FSet A) :=
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match dec (subset X Y) with
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| inl _ => true
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| inr _ => false
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end.
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Definition intersection (X Y : FSet A) : FSet A := comprehension (fun a => isIn_b a Y) X.
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End decidable_A.
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