proposition: Lemma F_alpha_mono (alpha: E0): strict_mono (F_ alpha).
proof: Proof. rewrite /strict_mono /F_ => n p Hnp; apply /ltP. apply F_alpha_mono; move: Hnp => /ltP //. Qed.
imports: mathcomp(all_ssreflect zify) Coq(Logic.Eqdep_dec Arith) hydras(DecPreOrder) hydras(T1 E0) hydras(primRec) hydras(F_alpha F_omega) gaia_hydras(T1Bridge GCanon GHprime)