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27 lines
1.3 KiB
27 lines
1.3 KiB
We choose:
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\begin{itemize}
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\item Triangle 1: a-b-c
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\item Triangle 2: a-c-d
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\item Triangle 3: c-d-e
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\end{itemize}
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\begin{align*}
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\varphi_{TC} \coloneqq &
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(e_{a = b} \land e_{b = c} \rightarrow e_{a = c}) \land \\
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& (e_{a = b} \land e_{a = c} \rightarrow e_{b = c}) \land \\
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& (e_{b = c} \land e_{a = c} \rightarrow e_{a = b}) \land \\
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&\\
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& (e_{a = c} \land e_{c = d} \rightarrow e_{a = d}) \land \\
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& (e_{a = c} \land e_{a = d} \rightarrow e_{c = d}) \land \\
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& (e_{c = d} \land e_{a = d} \rightarrow e_{a = c}) \land \\
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&\\
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& (e_{c = e} \land e_{c = d} \rightarrow e_{d = e}) \land \\
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& (e_{c = e} \land e_{d = e} \rightarrow e_{c = d}) \land \\
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& (e_{c = d} \land e_{d = e} \rightarrow e_{c = e})
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\end{align*}
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\begin{align*}
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\hat\varphi_{E} \coloneqq
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(e_{a=b} \; \lor \; e_{a=d} \imp (e_{b=c} \; \land \; \neg e_{c = e}\; \land \; \neg e_{e = d})
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\end{align*}
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\begin{align*}
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\varphi_{prop} \coloneqq \varphi_{TC} \land \hat\varphi_{E}
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\end{align*}
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