proposition: Lemma nb_surj_0p p: nb_surj 0 p.+1 = 0.
proof: Proof. rewrite /nb_surj /bin_conv_inv; set s := \sum_(i< _) _. suff: s = 0 by move => ->; apply: mulr0. transitivity (\sum_(i < p.+2) (-1%:Z) ^+ i *+ 'C(p.+1, i)). by apply :eq_bigr => i _; rewrite expn0 mulr1. rewrite F26a bin_small //. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq choice fintype binomial) mathcomp(bigop ssralg poly ssrint) gaia(ssete7)