proposition: Lemma ord_negl_p7 x y: \0o <o x -> \0o <o y -> odegree x <o odegree y -> x <<o y.
proof: Proof. move => xp yp. rewrite (odegree_of_pos xp) (odegree_of_pos yp). move: (the_cnf_p0 (proj32_1 xp))(the_cnf_p0 (proj32_1 yp)). move:(the_cnf_p2 xp)(the_cnf_p2 yp). set p:= (cnf_size _); set q := (cnf_size _). move => [pN sp][nN sn] [ax1 {2} <- ] [ax2 {2} <-] h. move: (proj44 ax1) (proj44 ax2); rewrite /cnf_val sp sn => qa qb. exact: (ord_negl_p8 qa qb pN nN h). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)