File: theorems.tex

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\chapter{Pre-proved Theorems}\input{theorems-intro}\section{Definitions}\THEOREM PMI\_DEF win
|- !a b. a <== b = b ==> a
\ENDTHEOREM
\section{Theorems}\THEOREM IMP\_REFL\_THM win
|- !x. x ==> x
\ENDTHEOREM
\THEOREM IMP\_TRANS\_THM win
|- !x y z. (x ==> y) /\ (y ==> z) ==> x ==> z
\ENDTHEOREM
\THEOREM PMI\_DEF win
|- !a b. a <== b = b ==> a
\ENDTHEOREM
\THEOREM PMI\_REFL\_THM win
|- !x. x <== x
\ENDTHEOREM
\THEOREM PMI\_TRANS\_THM win
|- !x y z. (x <== y) /\ (y <== z) ==> x <== z
\ENDTHEOREM