proposition: Lemma incl_bigcup_compat_list_eq (T U : Type) (h1 h2 : T) (t1 t2 : list T) (F G : T -> set U) : F h1 <--> G h2 -> \bigcup_(x in t1) F x <--> \bigcup_(x in t2) G x -> \bigcup_(x in h1 :: t1) F x <--> \bigcup_(x in h2 :: t2) G x.
proof: Proof. intros Hs1 Hs2. split; eapply incl_bigcup_compat_list. - rewrite Hs1. eapply subset_refl. - rewrite Hs2. eapply subset_refl. - rewrite Hs1. eapply subset_refl. - rewrite Hs2. eapply subset_refl. Qed.
imports: mathcomp.ssreflect.ssreflect Classes.RelationClasses Classes.Morphisms List Tactics mathcomp(ssrfun ssrbool ssrnat seq)