proposition: Lemma B_N2N: Nat \Eq (coarse Nat).
proof: Proof. move: bn_nn_inj =>[ha hb hc]. move: (inj_source_smaller ha); rewrite hb hc => hd. apply/card_eqP; exact: (cleA N2N_part1 hd). Qed.
imports: mathcomp(ssreflect ssrbool eqtype ssrfun)