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| | ===Evaluation Rule 1=== | | ===Evaluation Rule 1=== |
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| − | ====Variant 1====
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| | | width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math> | | | width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math> |
| | | width="84%" style="border-top:1px solid black" | <math>f, g ~:~ X \to \underline\mathbb{B}</math> | | | width="84%" style="border-top:1px solid black" | <math>f, g ~:~ X \to \underline\mathbb{B}</math> |
| − | |- style="height:40px"
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| − | | <math>\text{and}\!</math>
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| − | | <math>x ~\in~ X</math>
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| − | |- style="height:40px"
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| − | | <math>\text{then}\!</math>
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| − | | <math>\text{the following are equivalent:}\!</math>
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| − | |}
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| − | {| align="center" cellpadding="0" cellspacing="0" width="100%"
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| − | |- style="height:40px"
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| − | | width="2%" style="border-top:1px solid black" |
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| − | | width="14%" style="border-top:1px solid black" | <math>\operatorname{E1a.}</math>
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| − | | width="64%" style="border-top:1px solid black" | <math>f(x) ~=~ g(x)</math>
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| − | | width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{E1a~:~V1a}</math>
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| − | |- style="height:20px"
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | | <math>\operatorname{E1b.}</math>
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| − | | <math>f(x) ~\Leftrightarrow~ g(x)</math>
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| − | | style="border-left:1px solid black; text-align:center" | <math>\operatorname{E1b~:~V1b}</math>
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| − | |- style="height:20px"
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:60px"
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| − | | <math>\operatorname{E1c.}</math>
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| − | | <math>\underline{((}~ f(x) ~,~ g(x) ~\underline{))}</math>
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| − | | style="border-left:1px solid black; text-align:center" |
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| − | <p><math>\operatorname{E1c~:~V1c}</math></p>
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| − | <p><math>\operatorname{E1c~:~$1a}</math></p>
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| − | |- style="height:20px"
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| − | | style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| − | |- style="height:40px"
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| − | | <math>\operatorname{E1d.}</math>
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| − | | <math>\underline{((}~ f ~,~ g ~\underline{))}^\$ (x)</math>
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| − | | style="border-left:1px solid black; text-align:center" | <math>\operatorname{E1d~:~$1b}</math>
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| − | |}
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| − | |}
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| − | <br>
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| − |
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| − | ====Variant 2====
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| − | <br>
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| − | {| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
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| − | {| align="center" cellpadding="0" cellspacing="0" width="100%"
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| − | |- style="height:40px; text-align:right"
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| − | | width="98%" | <math>\text{Evaluation Rule 1}\!</math>
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| − | | width="2%" |
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| − | |}
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| − | {| align="center" cellpadding="0" cellspacing="0" width="100%"
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| − | |- style="height:40px"
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| − | | width="2%" style="border-top:1px solid black" |
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| − | | width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math>
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| − | | width="84%" style="border-top:1px solid black" | <math>s, t ~\text{are sentences about things in the universe}~ X</math>
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| − | |- style="height:40px"
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| − | | <math>f, g ~\text{are propositions} ~:~ X \to \underline\mathbb{B}</math>
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| | |- style="height:40px" | | |- style="height:40px" |
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