proposition: Lemma fun_on_quotient_pr3 r f x: equivalence r -> inc x (substrate r) -> compatible_with_equiv f r -> Vf f x = Vf (fun_on_quotient r f) (Vf (canon_proj r) x).
proof: Proof. move=> er xs co; rewrite - compfV; last by aw. by rewrite compose_foq_proj. by apply: composable_fun_projc. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)