proposition: Lemma prl_r3_prop6 i j (lij: gle prl_r3_nr i j) : prl_same_data (prl_restr (prl_r3_prop5 lij)) (prl_r3_systemi i).
proof: Proof. move/sub_gleP: (lij) => [iL jL r1]. have Hu:= (prl_r3_prop4 jL). apply:prl_same_dataT (prl_r3_prop5b (sub_trans r1 Hu) iL). apply:prl_same_dataT (projective_limit_restr_double_Iv Hu r1). apply:prl_restr_Iv2. exact: (prl_same_dataS (prl_r3_prop5b Hu jL)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)