5 Let L= {f2,c} be a language including a binary function and a constant, and let...
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5 Let L= {f2,c} be a language including a binary function and a constant, and let TG be the set of sentences • (Vx)(Vy) (Vz)(= ffxyzfxfyz). • (Vx)(= fxcx). • (Vx)(= fcxx). (Vx) (y)(= fxyc A = fyxc). Prove that TG (Vr) (Vy)(= fayfyr). (Hint: Soundness.) 5 Let L= {f2,c} be a language including a binary function and a constant, and let TG be the set of sentences • (Vx)(Vy) (Vz)(= ffxyzfxfyz). • (Vx)(= fxcx). • (Vx)(= fcxx). (Vx) (y)(= fxyc A = fyxc). Prove that TG (Vr) (Vy)(= fayfyr). (Hint: Soundness.)
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