@@ -1604,12 +1604,12 @@ definitions of the following standard arithmetic operators.
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\index {EXP, the HOL constant@\holtxt {EXP}, the \HOL {} constant}
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\index { addition, in HOL logic@\holtxt {+} (addition, in \HOL {} logic)}
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\index { subtraction, in HOL logic@\holtxt {-} (subtraction, in \HOL {} logic)}
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- \index { multiplication, in HOL logic@\holtxt {*} (multiplication, in \HOL {} logic)}
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+ \index { multiplication, in HOL logic@\holtxt {*} (multiplication, in \HOL {} logic)!on natural numbers }
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\index { exponentiation, in HOL logic@\holtxt {**} (exponentiation, in \HOL {} logic)}
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\index {addition, in HOL logic@addition, in \HOL {} logic}
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\index {subtraction, in HOL logic@subtraction, in \HOL {} logic}
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- \index {multiplication, in HOL logic@multiplication, in \HOL {} logic}
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- \index {exponentiation, in HOL logic@exponentiation, in \HOL {} logic}
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+ \index {multiplication, in HOL logic@multiplication, in \HOL {} logic!on natural numbers }
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+ \index {exponentiation, in HOL logic@exponentiation, in \HOL {} logic!on natural numbers }
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\begin {alltt }
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>>__ open arithmeticTheory
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##thm ADD
@@ -1922,6 +1922,8 @@ similar operations on the natural numbers, and on the real numbers.
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The constants defined in the integer theory include those found in the
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following table.
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+ \index {multiplication, in HOL logic@multiplication, in \HOL {} logic!on integers}
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+ \index { multiplication, in HOL logic@\holtxt {*} (multiplication, in \HOL {} logic)!on integers}
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\begin {center }
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{\small
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\begin {tabular }{@{}cccc}
@@ -2757,6 +2759,7 @@ paths, and finite strings.
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>>__ open listTheory
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>>__ show_numeral_types := false
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+ \index {lists, the HOL theory of@lists, the \HOL {} theory of!constructors}
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\HOL {} lists are inductively defined finite sequences where each
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element in a list has the same type. The theory \ml {list} introduces
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the unary type operator $ \alpha \; \konst {list}$ by a type definition
@@ -2797,6 +2800,8 @@ fundamental theorems about lists are proved and stored in the theory
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\index {axioms!non-primitive, of HOL logic@non-primitive, of \HOL {} logic!for lists}
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\index {induction theorems, in HOL logic@induction theorems, in \HOL {} logic!for lists}
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\index {characterizing theorem!for lists}
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+ \index {lists, the HOL theory of@lists the \HOL {} theory of!initiality theorem}
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+ \index {lists, the HOL theory of@lists the \HOL {} theory of!induction theorem}
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\begin {alltt }
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##thm list_Axiom
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##thm list_INDUCT
@@ -4487,7 +4492,7 @@ infix), inversion (\holtxt{inv}, or $\_^{\mathsf{T}}$ (suffix superscript `T')),
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\noindent Set operations lifted to work on relations include subset
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(\holtxt {RSUBSET}, or $ \subseteq \subr $ , infix), union (\holtxt {RUNION}, or $ \cup \subr $ , infix),
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intersection (\holtxt {RINTER}, or $ \cap \subr $ , infix), complement (\holtxt {RCOMPL}),
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- and universe (\holtxt {RUNIV}, or $ \mathbb {U}\subr $ ).
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+ and universe (\holtxt {RUNIV}, or $ \mathbb {U}\subr $ ).\label { def:rsubset }
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%
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\begin {hol }
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\begin {alltt }
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