proposition: Lemma ext2_pr7 E E' g z: bijection_prop g E E' -> inc z (\Po (\Po E)) -> extension_p3 (inverse_fun g) (extension_p3 g z) = z.
proof: Proof. move => ha zz; move: (ha) => [hb hc _]. rewrite (ext2_pr6 ha (inverse_bij_bp ha) zz) (bij_left_inverse hb) hc. have ip:= (identity_bp E). by rewrite (ext2_pr2 ip zz) /extension_p2 etp_identity etp_identity idV. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)