Question

Give proofs for the theorems of $\mathscr{F}^\omega$ stated below. Use appropriate analogues of the derived rules of inference of $$\$ 21$$. $\vdash x_\tau=x_q$

   Give proofs for the theorems of $\mathscr{F}^\omega$ stated below. Use appropriate analogues of the derived rules of inference of $$\$ 21$$.
$\vdash x_\tau=x_q$

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Computer Science & Applied Mathematics)

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Computer Science & Applied Mathematics)

Peter B. Andrews 1st Edition

Chapter 5, Problem 1

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Step 1

This statement asserts that $x_\tau$ is logically equivalent to $x_q$ in the formal system $\mathscr{F}^\omega$. This is a statement of equality within the logical framework, and we need to establish this using the rules and axioms available in the system. Show more…

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Give proofs for the theorems of $\mathscr{F}^\omega$ stated below. Use appropriate analogues of the derived rules of inference of $$\$ 21$$. $\vdash x_\tau=x_q$

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