From 48d958f2ff9fd51d40b8cc1386da57fe2078d2e7 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Wed, 28 Sep 2016 10:05:48 +0200 Subject: [PATCH] Induction principle for finite sets with Leibniz equality. --- prelude/fin_collections.v | 3 +++ 1 file changed, 3 insertions(+) diff --git a/prelude/fin_collections.v b/prelude/fin_collections.v index 0aaf5bd51..8b4938358 100644 --- a/prelude/fin_collections.v +++ b/prelude/fin_collections.v @@ -157,6 +157,9 @@ Proof. apply Hadd. set_solver. apply IH; set_solver. - by rewrite HX. Qed. +Lemma collection_ind_L `{!LeibnizEquiv C} (P : C → Prop) : + P ∅ → (∀ x X, x ∉ X → P X → P ({[ x ]} ∪ X)) → ∀ X, P X. +Proof. apply collection_ind. by intros ?? ->%leibniz_equiv_iff. Qed. (** * The [collection_fold] operation *) Lemma collection_fold_ind {B} (P : B → C → Prop) (f : A → B → B) (b : B) : -- GitLab