proposition: Lemma CNF_simple_bdn3 x (v := (P (the_CNF_simpl x))) (y:= inv_psi_omega v): \0o <o x -> x <o Gamma_0 -> [/\ pairp y, (P y) <o x, (Q y) <o x & Spsi (P y) (Q y) = omega0 ^o v ].
proof: Proof. move => pa pc. move:(the_CNF_simplP pa) => ha. move:(CNF_simple_p2 ha) =>[hb hc hd]. move:(inv_psi_omega_p2 (proj31 hb) (ole_ltT hb pc)) => [qa qb qc qd]. split; [exact | exact: (olt_leT qb hd) | exact: (olt_leT qc hd) | exact]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)