proposition: Lemma prJ_recov (a b:Set) (x:a \times b): pairC (pr1C x) (pr2C x) = x.
proof: Proof. apply: R_inj; rewrite prJ_prop pr1C_prop pr2C_prop. rewrite (setX_pair (A:=a)(B:=b)) //; by apply: R_inc. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)