proposition: Lemma inl_map2_prop S S' u (g := inductive_limit_fun S S' u): inl_same_index S S' -> inl_map2_compat S S' u -> inl_map2_property S S' u g.
proof: Proof. move => ha hb. move: (inl_map_prop (inl_map2_prop1 ha hb)) => [qa qb]. split => // i iI. move:(iI); rewrite (inl_same_index_same_I ha)=> iI'. have idx: inc i (domain (inl_map2_aux S' u)) by rewrite /inl_map2_aux Lgd. rewrite - qb // /inl_map2_aux LgV//. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)