proposition: Lemma inl_restr_cf_ev S J (H:sub_right_directed J (isr S)) i x: inc i J -> inc x (Vg (isE S) i) -> Vf (inl_restr_cf H) (class (inl_equiv (inl_restr H)) (Pair.J x i)) = class (inl_equiv S) (Pair.J x i).
proof: Proof. move => iI xE. have xE': inc x (Vg (isE (inl_restr H)) i) by rewrite /= LgV. rewrite (inl_inductive_map_ev (inl_restr_cf_compat H) iI xE'). by rewrite LgV // inl_can_fun_ev //; move: (proj1 H _ iI); rewrite is_substrate_r. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)