pooj4
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Trouble working through Set theory, Logic, and their Limitations by Maurice Machover. Particularly these
1. $\sigma \vDash \alpha \rightarrow \forall x\alpha$ where $x$ does not occur in a free $\alpha$
2. $\sigma \vDash s_1 = t_1 \rightarrow ... \rightarrow s_n = t_n \rightarrow fs_1...s_n=ft_1...t_n$
3. $\sigma \vDash \forall x \alpha \rightarrow \alpha(x/t)$ (appealing to the fact that generally $\alpha(x/t)^\sigma = {\alpha}^{\sigma(x/t^\sigma )})$
1. $\sigma \vDash \alpha \rightarrow \forall x\alpha$ where $x$ does not occur in a free $\alpha$
2. $\sigma \vDash s_1 = t_1 \rightarrow ... \rightarrow s_n = t_n \rightarrow fs_1...s_n=ft_1...t_n$
3. $\sigma \vDash \forall x \alpha \rightarrow \alpha(x/t)$ (appealing to the fact that generally $\alpha(x/t)^\sigma = {\alpha}^{\sigma(x/t^\sigma )})$