proposition: Lemma up2_f0: f \0c = \0c.
proof: Proof. have pa: ~ (inc \0c Nat /\ \0c <> \0c) by move => []. have pb: ~ (exists y, [/\ inc y Nat, y <> \0c & \0c = singleton y]). by move => [y [yb ynz yv]]; move:(set1_1 y); rewrite - yv; case; case. by rewrite /f /universe_permutation_fun; Ytac0; Ytac0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)