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Directory:Jon Awbrey/Papers/Propositions As Types
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Revision as of 02:31, 28 March 2009
16 bytes added
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02:31, 28 March 2009
→Conjunction Calculus
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spacing
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<p><math>\begin{array}{ll}
<p><math>\begin{array}{ll}
−
\text{R2.} & A \xrightarrow{~\bigcirc_A~} \operatorname{T};
+
\text{R2.} & A
~
\xrightarrow{~\bigcirc_A~}
~
\operatorname{T};
\\[8pt]
\\[8pt]
−
\text{R3a.} & A \land B \xrightarrow{~\pi_{A, B}~} A,
+
\text{R3a.} & A \land B
~
\xrightarrow{~\pi_{A, B}~}
~
A,
\\[8pt]
\\[8pt]
−
\text{R3b.} & A \land B \xrightarrow{~\pi'_{A, B}~} B,
+
\text{R3b.} & A \land B
~
\xrightarrow{~\pi'_{A, B}~}
~
B,
\\[8pt]
\\[8pt]
−
\text{R3c.} & \dfrac{C \xrightarrow{~f~} A \quad C \xrightarrow{~g~} B}{C \xrightarrow{~\langle f, g \rangle~} A \land B}.
+
\text{R3c.} & \dfrac{
~
C
~
\xrightarrow{~f~}
~
A \quad C
~
\xrightarrow{~g~}
~
B
~
}{C
~
\xrightarrow{~\langle f, g \rangle~}
~
A \land B}.
\end{array}</math></p>
\end{array}</math></p>
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Jon Awbrey
12,089
edits