Give proofs for the theorems of ℱ^ωstated below. Use appropriate analogues of the derived rules

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Step 1:u000AUnderstand the theorem to be proved:u000AThe theorem states that $u005Cvdash x_u005Ctau u003D y_{u005Cmathrm

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