# HG changeset patch # User kleing # Date 1052744803 -7200 # Node ID dd80d4654926d363c78a2a34618689f4f1f755e9 # Parent 9d1f027eb4e8706fb590f5f1c9e6956227478aa5 moved % comments out of ttboxes diff -r 9d1f027eb4e8 -r dd80d4654926 doc-src/HOL/HOL.tex --- a/doc-src/HOL/HOL.tex Mon May 12 14:49:08 2003 +0200 +++ b/doc-src/HOL/HOL.tex Mon May 12 15:06:43 2003 +0200 @@ -385,14 +385,14 @@ \tdx{iffD1} [| P=Q; P |] ==> Q \tdx{iffD2} [| P=Q; Q |] ==> P \tdx{iffE} [| P=Q; [| P --> Q; Q --> P |] ==> R |] ==> R -% -%\tdx{eqTrueI} P ==> P=True -%\tdx{eqTrueE} P=True ==> P \subcaption{Logical equivalence} \end{ttbox} \caption{Derived rules for HOL} \label{hol-lemmas1} \end{figure} +% +%\tdx{eqTrueI} P ==> P=True +%\tdx{eqTrueE} P=True ==> P \begin{figure} @@ -846,15 +846,15 @@ \tdx{Union_Un_distrib} Union(A Un B) = (Union A) Un (Union B) \tdx{Int_Union} A Int (Union B) = (UN C:B. A Int C) -%\tdx{Un_Union_image} (UN x:C.(A x) Un (B x)) = Union(A``C) Un Union(B``C) \tdx{Inter_Un_distrib} Inter(A Un B) = (Inter A) Int (Inter B) \tdx{Un_Inter} A Un (Inter B) = (INT C:B. A Un C) -%\tdx{Int_Inter_image} (INT x:C.(A x) Int (B x)) = Inter(A``C) Int Inter(B``C) + \end{ttbox} \caption{Set equalities} \label{hol-equalities} \end{figure} - +%\tdx{Un_Union_image} (UN x:C.(A x) Un (B x)) = Union(A``C) Un Union(B``C) +%\tdx{Int_Inter_image} (INT x:C.(A x) Int (B x)) = Inter(A``C) Int Inter(B``C) Figures~\ref{hol-set1} and~\ref{hol-set2} present derived rules. Most are obvious and resemble rules of Isabelle's ZF set theory. Certain rules, such @@ -1155,10 +1155,10 @@ $[\alpha\,set, \alpha\To\beta\,set]\To(\alpha\times\beta)set$ & & general sum of sets \end{constants} -\begin{ttbox}\makeatletter %\tdx{fst_def} fst p == @a. ? b. p = (a,b) %\tdx{snd_def} snd p == @b. ? a. p = (a,b) %\tdx{split_def} split c p == c (fst p) (snd p) +\begin{ttbox}\makeatletter \tdx{Sigma_def} Sigma A B == UN x:A. UN y:B x. {\ttlbrace}(x,y){\ttrbrace} \tdx{Pair_eq} ((a,b) = (a',b')) = (a=a' & b=b')