proposition: Lemma cnf_sum_nz x y: cnfp x -> cnfp_nz y -> x +f y <> \0f.
proof: Proof. move => ox ynz sz. move: (cnf_sum_range ox ynz); rewrite sz range_set0 /cnf_sum_mons. move/esym /setU2_eq0P /proj2; set u := J _ _ => h. by move:(set1_1 u); rewrite h => /in_set0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)