proposition: Lemma fusc_quo_pow2p n: natp n -> fusc_quo (\2c ^c n -c \1c) = BQ_of_nat n.
proof: Proof. move => nN; rewrite /fusc_quo. have pN: natp (\2c ^c n) by fprops. have pnz: (\2c ^c n) <> \0c by apply: (cpow_nz card2_nz). rewrite (fusc_pred_pow2 nN) - (cpred_pr4 (CS_nat pN)). by rewrite -(proj2 (cpred_pr pN pnz))(fusc_pow2 nN) (BQdiv_x1 (QS_of_nat nN)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)