\chapter{Pre-proved Theorems}
\input{theorems-intro}
\section{Theorems}
\THEOREM CURRY\_ONE\_ONE\_THM -
|- (CURRY f = CURRY g) = (f = g)
\ENDTHEOREM
\THEOREM CURRY\_UNCURRY\_THM -
|- !f. CURRY(UNCURRY f) = f
\ENDTHEOREM
\THEOREM PEXISTS\_THM -
|- !f. (?x y. f x y) = (?(x,y). f x y)
\ENDTHEOREM
\THEOREM PFORALL\_THM -
|- !f. (!x y. f x y) = (!(x,y). f x y)
\ENDTHEOREM
\THEOREM UNCURRY\_CURRY\_THM -
|- !f. UNCURRY(CURRY f) = f
\ENDTHEOREM
\THEOREM UNCURRY\_ONE\_ONE\_THM -
|- (UNCURRY f = UNCURRY g) = (f = g)
\ENDTHEOREM
