proposition: Lemma IB_rel_i rho ipl ipr ia ib ic id a b c d : rho ipl=Pair a b -> rho ipr=Pair c d -> rho ia=Num a -> rho ib=Num b -> rho ic=Num c -> rho id=Num d -> h10upc_sem_direct ((a,b),(c,d)) -> rho ⊨ rel ipl ipr ia ib ic id.
proof: Proof. intros Hpl Hpr Ha Hb Hc Hd Habcd. split. 1:split. - eapply IB_P_i; eauto. - eapply IB_P_i; eauto. - cbn. rewrite Hpl, Hpr. apply Habcd. Qed.
imports: Undecidability.DiophantineConstraints(H10C) Undecidability.DiophantineConstraints.Util(H10UPC_facts) Undecidability.FOL(Syntax.Facts Deduction.FullNDFacts Semantics.Tarski.FullSoundness Semantics.Tarski.FullFacts Syntax.BinSig) Undecidability.Shared(Dec) Undecidability.Shared.Libs.PSL(Numbers) Coq(Arith Lia List) Undecidability.Synthetic.Definitions