proposition: Lemma F_alpha_not_PR alpha (Hnf: T1nf alpha == true): LE T1omega alpha -> isPR 1 (@T1F_ alpha Hnf) -> False.
proof: Proof. rewrite /T1F_ => Halpha; apply F_alpha_not_PR_E0; rewrite /E0le => /=; by destruct Halpha. 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)