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| | ===Proof Schemata=== | | ===Proof Schemata=== |
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| − | <br>
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| − | {| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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| − | | align="left" style="border-left:1px solid black;" width="50%" |
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| − | | align="right" style="border-right:1px solid black;" width="50%" | <math>\text{Definition 1}\!</math>
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| − | | colspan="2" style="border-left:1px solid black; border-right:1px solid black; border-top:1px solid black" |
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| − | <math>\begin{array}{ll}
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| − | \text{If} & Q \subseteq X
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| − | \\
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| − | \\
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| − | \text{then} & \upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}
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| − | \\
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| − | \\
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| − | \text{such that:}
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| − | \end{array}</math>
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| − | | align="left" style="border-left:1px solid black; border-top:1px solid black" width="50%" |
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| − | <math>\begin{array}{ll}
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| − | \text{D1a.} & \upharpoonleft Q \upharpoonright (x) ~\Leftrightarrow~ x \in Q
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| − | \end{array}</math>
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| − | | align="right" style="border-right:1px solid black; border-top:1px solid black" width="50%" |
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| − | <math>\forall x \in X</math>
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| − | |}
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| | | style="border-left:1px solid black" | <math>\text{R2a.}\!</math> | | | style="border-left:1px solid black" | <math>\text{R2a.}\!</math> |
| | | <math>\upharpoonleft Q \upharpoonright (x)</math> | | | <math>\upharpoonleft Q \upharpoonright (x)</math> |
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| − | |}
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| − | <br>
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| − | {| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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| − | |-
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| − | | align="left" style="border-left:1px solid black" width="20%" |
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| − | | align="left" width="60%" |
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| − | | align="right" style="border-right:1px solid black" width="20%" | <math>\text{Rule 1}\!</math>
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| − | | style="border-left:1px solid black; border-top:1px solid black" | <math>\text{If}\!</math>
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| − | | style="border-top:1px solid black" | <math>Q \subseteq X,</math>
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| − | | style="border-right:1px solid black; border-top:1px solid black" |
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| − | | style="border-left:1px solid black" | <math>\text{then}\!</math>
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| − | | <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B},</math>
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| − | | style="border-right:1px solid black" |
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| − | | style="border-left:1px solid black" | <math>\text{and if}\!</math>
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| − | | <math>x \in X,</math>
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| − | | style="border-right:1px solid black" |
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| − | | style="border-left:1px solid black" | <math>\text{then}\!</math>
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| − | | <math>\text{the following are equivalent:}\!</math>
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| − | | style="border-left:1px solid black; border-top:1px solid black" | <math>\text{R1a.}\!</math>
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| − | | style="border-top:1px solid black" | <math>x \in Q.</math>
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| − | | style="border-right:1px solid black; border-top:1px solid black" |
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| − | | style="border-left:1px solid black" | <math>\text{R2a.}\!</math>
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| − | | <math>\upharpoonleft Q \upharpoonright (x).</math>
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| | | style="border-right:1px solid black" | | | | style="border-right:1px solid black" | |
| | |} | | |} |
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| | <br> | | <br> |