proposition: Fact nat_is_PAeq_model : forall ax rho, PAeq ax -> sat interp_nat rho ax.
proof: Proof. intros rho psi []. now apply nat_is_FA_model. all: cbn; try congruence. apply nat_induction. Qed.
imports: Undecidability.FOL.Arithmetics(FA Signature) Undecidability.FOL(PA) Lia List Vector