proposition: Lemma prl_subsets_prop_I2v S S' M (H:prl_subfam_hyp S M) (H':prl_subfam_hyp S' M) : prl_same_data S S' -> prl_same_data (projective_system_subsets H) (projective_system_subsets H').
proof: Proof. move:(prl_subsets_prop H) => [ra rb rc rd]. move:(prl_subsets_prop H') => [ra' rb' rc' rd']. rewrite /prl_same_data ra rc rd ra' rc' rd' => - [ea eb ec]. by rewrite /prl_subfam_fct eb ec. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)