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21 lines
920 B
21 lines
920 B
\setlength\subproofhorizspace{1.7em}
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\begin{logicproof}{2}
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\forall x \; P(x) \lor \forall x \; Q(x) & prem.\\
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\begin{subproof}
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\forall x \; P(x) & ass.\\
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\begin{subproof}
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\llap{$t\enspace \;$} P(t) & $\forall \mathrm{e}$ 2\\
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P(t) \lor Q(t) & $\lor \mathrm{i}_1$ 3
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\end{subproof}
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\forall y \; (P(y) \lor Q(y)) & $\forall \mathrm{i}$ 3-4
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\end{subproof}
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\begin{subproof}
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\forall x \; Q(x) & ass.\\
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\begin{subproof}
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\llap{$s\enspace \;$} Q(s) & $\forall \mathrm{e}$ 6\\
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P(s) \lor Q(s) & $\lor \mathrm{i}_2$ 7
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\end{subproof}
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\forall y \; (P(y) \lor Q(y)) & $\forall \mathrm{i}$ 7-8
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\end{subproof}
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\forall y \; (P(y) \lor Q(y)) & $\lor \mathrm{e}$ 1,2-5,6-9
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\end{logicproof}
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