proposition: Lemma the_cnf_p0_nz x (y:= the_cnf x): \0o <o x -> cnfp_nz y /\ cnf_val y = x.
proof: Proof. move =>[/proj32 ox /nesym xz]; move: (the_cnf_p0 ox) => [ha hb]; split => //. by split => // az; case: xz; rewrite -hb -/y az cnf_val0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)