proposition: Lemma all_equiv { p : peirce } (phi psi : form') A : (forall t, A ⊢ phi[t..] <-> A ⊢ psi[t..]) -> (A ⊢ ∀ phi) <-> (A ⊢ ∀ psi).
proof: Proof. intros H1. split; intros H2; apply AllI. all: edestruct (nameless_equiv_all A) as [x ->]; apply H1; auto. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Syntax.Asimpl Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Deduction.FullNDFacts Undecidability.FOL.Sets(binZF ZF) Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability(Shared.ListAutomation) Morphisms Undecidability.FOL(Reductions.PCPb_to_ZFeq)