proposition: Lemma same_cover_at f x y z (i := cover_at f y): partition_w_fam f x -> inc y x -> inc z (Vg f i) -> cover_at f z = i.
proof: Proof. move => pf yx zi. exact: (cover_at_pr pf (proj2 (cover_at_in pf yx)) zi). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)