proposition: Lemma satis_atom_subst_compat phi : satis phi[s/atom] -> satis phi .
proof: Proof. Proof using Hresp. intros (D&I&rho&H). unshelve eapply sat_atom_subst_compat in H. 1:exact 0. do 3 eexists. apply H. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Syntax.Theories Undecidability.FOL.Semantics.Tarski.FragmentCore Undecidability(Shared.ListAutomation) Vector Lia