proposition: Lemma inl_subsets_prop_Iv S M (H H':inl_subfam_hyp S M) : inl_same_data (inductive_system_subsets H) (inductive_system_subsets H').
proof: Proof. move:(inl_subsets_prop H) => [ra rb rc rd]. move:(inl_subsets_prop H') => [ra' rb' rc' rd']. by rewrite /inl_same_data ra rc rd. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)