Hip to be square (14 points)

Give a formal proof that, if integers n and m are squares, then nm is a square. In addition to the inference rules discussed in class, you can also rewrite an algebraic expression to equivalent ones using the rule "Algebra".

Please use inference rules listed below:

Excluded Middle .. AV-A Direct Proof Modus Ponens B Elim A Intro A A B .. A B Intro V Elim A. AVB A . AVB BV A Elim V Intro 3 Vr P(x) . P(a) for any a P(c) for some c 3r P(x) Intro V Let a be arbitrary... P(a) (If no other name in P depends on a) : Vr P(r) Elim 3 3r P(r) list dependencies for e .. P(c) for some special c Excluded Middle .. AV-A Direct Proof Modus Ponens B Elim A Intro A A B .. A B Intro V Elim A. AVB A . AVB BV A Elim V Intro 3 Vr P(x) . P(a) for any a P(c) for some c 3r P(x) Intro V Let a be arbitrary... P(a) (If no other name in P depends on a) : Vr P(r) Elim 3 3r P(r) list dependencies for e .. P(c) for some special c