proposition: Lemma specification_bot_impl_bot_with_eq : forall t, (t ⊩ ⊥ → ⊥) -> exists π', t ★ u·π ⪰ u ★ π'.
proof: Proof. intros t Ht. assert (t ★ u·π ∈ ⫫) as Hbot. Ksolve. start. rewrite Hpole. exists π. now left. rewrite Hpole in Hbot. destruct Hbot as [π' Hbot]. now exists π'. Qed.
imports: ClassicalRealizability.Tactics