proposition: Lemma Cantor_eta_pr r1 r2: eta_like r1 -> eta_like r2 -> r1 \Is r2.
proof: Proof. move => h1 h2. move: (esym(proj2 h1)); rewrite aleph0_pr1 => /card_eqP [f fp]. move: (esym(proj2 h2)); rewrite aleph0_pr1 => /card_eqP [g gp]. move: ( EP_fun_pr fp gp h1 h2) => h. by exists (EP_fun r1 r2 f g). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)