diff -r a931f1b45151 -r 1b3cddf41b2d doc-src/Logics/FOL.tex --- a/doc-src/Logics/FOL.tex Thu Nov 11 12:44:43 1993 +0100 +++ b/doc-src/Logics/FOL.tex Thu Nov 11 13:18:49 1993 +0100 @@ -47,30 +47,30 @@ (see~\S\ref{fol-int-prover}). See the files \ttindexbold{FOL/ifol.thy}, \ttindexbold{FOL/ifol.ML} and -\ttindexbold{FOL/int-prover.ML} for complete listings of the rules and +\ttindexbold{FOL/intprover.ML} for complete listings of the rules and derived rules. \begin{figure} \begin{center} \begin{tabular}{rrr} - \it name &\it meta-type & \it description \\ - \idx{Trueprop}& $o\To prop$ & coercion to $prop$\\ - \idx{Not} & $o\To o$ & negation ($\neg$) \\ - \idx{True} & $o$ & tautology ($\top$) \\ - \idx{False} & $o$ & absurdity ($\bot$) + \it name &\it meta-type & \it description \\ + \idx{Trueprop}& $o\To prop$ & coercion to $prop$\\ + \idx{Not} & $o\To o$ & negation ($\neg$) \\ + \idx{True} & $o$ & tautology ($\top$) \\ + \idx{False} & $o$ & absurdity ($\bot$) \end{tabular} \end{center} \subcaption{Constants} \begin{center} \begin{tabular}{llrrr} - \it symbol &\it name &\it meta-type & \it precedence & \it description \\ + \it symbol &\it name &\it meta-type & \it precedence & \it description \\ \idx{ALL} & \idx{All} & $(\alpha\To o)\To o$ & 10 & - universal quantifier ($\forall$) \\ + universal quantifier ($\forall$) \\ \idx{EX} & \idx{Ex} & $(\alpha\To o)\To o$ & 10 & - existential quantifier ($\exists$) \\ + existential quantifier ($\exists$) \\ \idx{EX!} & \idx{Ex1} & $(\alpha\To o)\To o$ & 10 & - unique existence ($\exists!$) + unique existence ($\exists!$) \end{tabular} \end{center} \subcaption{Binders} @@ -82,12 +82,12 @@ \indexbold{*"-"-">} \indexbold{*"<"-">} \begin{tabular}{rrrr} - \it symbol & \it meta-type & \it precedence & \it description \\ - \tt = & $[\alpha,\alpha]\To o$ & Left 50 & equality ($=$) \\ - \tt \& & $[o,o]\To o$ & Right 35 & conjunction ($\conj$) \\ - \tt | & $[o,o]\To o$ & Right 30 & disjunction ($\disj$) \\ - \tt --> & $[o,o]\To o$ & Right 25 & implication ($\imp$) \\ - \tt <-> & $[o,o]\To o$ & Right 25 & biconditional ($\bimp$) + \it symbol & \it meta-type & \it precedence & \it description \\ + \tt = & $[\alpha,\alpha]\To o$ & Left 50 & equality ($=$) \\ + \tt \& & $[o,o]\To o$ & Right 35 & conjunction ($\conj$) \\ + \tt | & $[o,o]\To o$ & Right 30 & disjunction ($\disj$) \\ + \tt --> & $[o,o]\To o$ & Right 25 & implication ($\imp$) \\ + \tt <-> & $[o,o]\To o$ & Right 25 & biconditional ($\bimp$) \end{tabular} \end{center} \subcaption{Infixes} @@ -95,16 +95,16 @@ \dquotes \[\begin{array}{rcl} formula & = & \hbox{expression of type~$o$} \\ - & | & term " = " term \\ - & | & term " \ttilde= " term \\ - & | & "\ttilde\ " formula \\ - & | & formula " \& " formula \\ - & | & formula " | " formula \\ - & | & formula " --> " formula \\ - & | & formula " <-> " formula \\ - & | & "ALL~" id~id^* " . " formula \\ - & | & "EX~~" id~id^* " . " formula \\ - & | & "EX!~" id~id^* " . " formula + & | & term " = " term \\ + & | & term " \ttilde= " term \\ + & | & "\ttilde\ " formula \\ + & | & formula " \& " formula \\ + & | & formula " | " formula \\ + & | & formula " --> " formula \\ + & | & formula " <-> " formula \\ + & | & "ALL~" id~id^* " . " formula \\ + & | & "EX~~" id~id^* " . " formula \\ + & | & "EX!~" id~id^* " . " formula \end{array} \] \subcaption{Grammar} @@ -735,8 +735,8 @@ and~\ttindex{ifE}. They permit natural proofs of theorems such as the following: \begin{eqnarray*} - if(P, if(Q,A,B), if(Q,C,D)) & \bimp & if(Q,if(P,A,C),if(P,B,D)) \\ - if(if(P,Q,R), A, B) & \bimp & if(P,if(Q,A,B),if(R,A,B)) + if(P, if(Q,A,B), if(Q,C,D)) & \bimp & if(Q,if(P,A,C),if(P,B,D)) \\ + if(if(P,Q,R), A, B) & \bimp & if(P,if(Q,A,B),if(R,A,B)) \end{eqnarray*} Proofs also require the classical reasoning rules and the $\bimp$ introduction rule (called~\ttindex{iffI}: do not confuse with~\ttindex{ifI}).