proposition: Lemma IB_erel_i rho ia ib ic id a b 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 ⊨ erel ia ib ic id.
proof: Proof. intros Ha Hb Hc Hd Habcd. exists (Pair c d), (Pair a b). eapply IB_rel_i. 1-2: reflexivity. all: easy. 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