proposition: Lemma IB_P_e rho p l r ip il ir : rho ip = p -> rho il = l -> rho ir = r -> rho ⊨ P ip il ir -> {a:nat & {b:nat & p = Pair a b /\ l = Num a /\ r = Num b}}.
proof: Proof. intros Hp Hl Hr [[[[(a&b&->)%(IB_P'_e Hp) (nl&<-)%(IB_N_e Hl)] (nr&<-)%(IB_N_e Hr)] HP4] HP5]. exists a, b; repeat split. - cbn in HP4. rewrite Hl,Hp in HP4. now rewrite HP4. - cbn in HP5. rewrite Hr,Hp in HP5. now rewrite HP5. 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