diff -r 49312d90cf1f -r aa0571fb96b9 doc-src/TutorialI/tutorial.ind --- a/doc-src/TutorialI/tutorial.ind Fri Jul 13 18:22:13 2001 +0200 +++ b/doc-src/TutorialI/tutorial.ind Fri Jul 13 18:28:46 2001 +0200 @@ -1,25 +1,28 @@ \begin{theindex} - \item \emph {$\forall \tmspace +\thinmuskip {.1667em}$}, \bold{3}, - \bold{189} + \item \emph {$\forall \tmspace +\thinmuskip {.1667em}$}, \bold{189} + \item \isasymforall, \bold{3} \item \ttall, \bold{189} - \item \emph {$\exists \tmspace +\thinmuskip {.1667em}$}, \bold{3}, - \bold{189} + \item \emph {$\exists \tmspace +\thinmuskip {.1667em}$}, \bold{189} + \item \isasymexists, \bold{3} \item \texttt{?}, \hyperpage{5}, \bold{189} \item \emph {$\varepsilon $}, \bold{189} \item \isasymuniqex, \bold{3}, \bold{189} \item \ttuniquex, \bold{189} - \item \emph {$\wedge $}, \bold{3}, \bold{189} + \item \emph {$\wedge $}, \bold{189} + \item \isasymand, \bold{3} \item {\texttt {\&}}, \bold{189} \item \texttt {=}, \bold{3} - \item \emph {$\DOTSB \relbar \joinrel \rightarrow $}, \bold{3}, - \bold{189} + \item \emph {$\DOTSB \relbar \joinrel \rightarrow $}, \bold{189} + \item \isasymimp, \bold{3} \item \texttt {-->}, \bold{189} - \item \emph {$\neg $}, \bold{3}, \bold{189} + \item \emph {$\neg $}, \bold{189} + \item \isasymnot, \bold{3} \item \verb$~$, \bold{189} \item \emph {$\not =$}, \bold{189} \item \verb$~=$, \bold{189} - \item \emph {$\vee $}, \bold{3}, \bold{189} + \item \emph {$\vee $}, \bold{189} + \item \isasymor, \bold{3} \item \ttor, \bold{189} \item \emph {$\circ $}, \bold{189} \item \emph {$\mid $}\nobreakspace {}\emph {$\mid $}, \bold{189} @@ -50,9 +53,9 @@ \item \ttAnd, \bold{189} \item \emph {$\equiv $}, \bold{23}, \bold{189} \item \texttt {==}, \bold{189} - \item \emph {$\rightleftharpoons $}, \bold{23}, \bold{189} - \item \emph {$\rightharpoonup $}, \bold{23}, \bold{189} - \item \emph {$\leftharpoondown $}, \bold{23}, \bold{189} + \item \emph {$\rightleftharpoons $}, \bold{24}, \bold{189} + \item \emph {$\rightharpoonup $}, \bold{24}, \bold{189} + \item \emph {$\leftharpoondown $}, \bold{24}, \bold{189} \item \emph {$\Rightarrow $}, \bold{3}, \bold{189} \item \texttt {=>}, \bold{189} \item \texttt {<=}, \bold{189} @@ -77,33 +80,27 @@ \indexspace - \item \isa {0}, \bold{20} - \item \texttt {0}, \bold{21} + \item \isa {0} (constant), \hyperpage{20, 21}, \hyperpage{133} + \item \isa {1} (symbol), \hyperpage{133} + \item \isa {2} (symbol), \hyperpage{133} \indexspace \item abandon proof, \bold{11} \item abandon theory, \bold{14} + \item \isa {abs} (constant), \hyperpage{135} \item \texttt {abs}, \bold{189} - \item \isa {abs_mult} (theorem), \bold{135} - \item \isa {add_2_eq_Suc} (theorem), \bold{133} - \item \isa {add_2_eq_Suc'} (theorem), \bold{133} + \item absolute value, \hyperpage{135} \item \isa {add_assoc} (theorem), \bold{134} \item \isa {add_commute} (theorem), \bold{134} - \item \isa {add_left_commute} (theorem), \bold{134} \item \isa {add_mult_distrib} (theorem), \bold{133} \item \texttt {ALL}, \bold{189} \item \isa {All} (constant), \hyperpage{93} \item \isa {allE} (theorem), \bold{65} \item \isa {allI} (theorem), \bold{64} - \item \isa {analz_Crypt_if} (theorem), \bold{186} - \item \isa {analz_idem} (theorem), \bold{180} - \item \isa {analz_mono} (theorem), \bold{180} - \item \isa {analz_synth} (theorem), \bold{180} - \item \isa {append_take_drop_id} (theorem), \bold{127} - \item apply, \bold{13} + \item \isacommand {apply} (command), \hyperpage{13} \item \isa {arg_cong} (theorem), \bold{80} - \item \isa {arith}, \bold{21} + \item \isa {arith} (method), \hyperpage{21}, \hyperpage{131} \item arithmetic, \hyperpage{20--21}, \hyperpage{31} \item \textsc {ascii} symbols, \bold{189} \item associative-commutative function, \hyperpage{158} @@ -152,15 +149,10 @@ \item \isa {classical} (theorem), \bold{57} \item closure \subitem reflexive and transitive, \hyperpage{96--98} - \item \isa {coinduct} (theorem), \bold{100} \item coinduction, \bold{100} \item \isa {Collect} (constant), \hyperpage{93} - \item \isa {Collect_mem_eq} (theorem), \bold{91} \item \isa {comp_def} (theorem), \bold{96} - \item \isa {comp_mono} (theorem), \bold{96} \item \isa {Compl_iff} (theorem), \bold{90} - \item \isa {Compl_partition} (theorem), \bold{90} - \item \isa {Compl_Un} (theorem), \bold{90} \item complement \subitem of a set, \hyperpage{89} \item composition @@ -171,22 +163,16 @@ \item \isa {conjI} (theorem), \bold{52} \item \isa {Cons}, \bold{7} \item \isa {constdefs}, \bold{23} - \item \isa {contrapos_nn} (theorem), \bold{57} - \item \isa {contrapos_np} (theorem), \bold{57} - \item \isa {contrapos_pn} (theorem), \bold{57} - \item \isa {contrapos_pp} (theorem), \bold{57} \item contrapositives, \hyperpage{57} \item converse \subitem of a relation, \bold{96} - \item \isa {converse_comp} (theorem), \bold{96} \item \isa {converse_iff} (theorem), \bold{96} \item CTL, \hyperpage{100--110} \indexspace \item \isa {datatype}, \hyperpage{7}, \hyperpage{36--42} - \item \isa {defer}, \bold{14} - \item \isacommand {defer} (command), \hyperpage{84} + \item \isacommand {defer} (command), \hyperpage{14}, \hyperpage{84} \item definition, \bold{23} \subitem unfolding, \bold{28} \item \isa {defs}, \bold{23} @@ -195,32 +181,26 @@ \subitem indefinite, \hyperpage{70} \item \isa {dest} (attribute), \hyperpage{86} \item destruction rules, \hyperpage{55} - \item \isa {Diff_disjoint} (theorem), \bold{90} \item \isa {diff_mult_distrib} (theorem), \bold{133} \item difference \subitem of sets, \bold{90} \item \isa {disjCI} (theorem), \bold{58} \item \isa {disjE} (theorem), \bold{54} \item \isa {div}, \bold{20} - \item \isa {div_le_mono} (theorem), \bold{133} - \item \isa {div_mult1_eq} (theorem), \bold{133} - \item \isa {div_mult2_eq} (theorem), \bold{133} - \item \isa {div_mult_mult1} (theorem), \bold{133} - \item divides relation, \bold{68}, \hyperpage{78}, \hyperpage{85--87} - \item \isa {DIVISION_BY_ZERO_DIV} (theorem), \bold{134} - \item \isa {DIVISION_BY_ZERO_MOD} (theorem), \bold{134} + \item divides relation, \hyperpage{68}, \hyperpage{78}, + \hyperpage{85--87}, \hyperpage{134} + \item division + \subitem by negative numbers, \hyperpage{135} + \subitem by zero, \hyperpage{134} + \subitem for type \protect\isa{nat}, \hyperpage{133} \item domain \subitem of a relation, \hyperpage{96} \item \isa {Domain_iff} (theorem), \bold{96} \item done, \bold{11} \item \isa {drule_tac} (method), \hyperpage{60}, \hyperpage{80} - \item \isa {dvd_add} (theorem), \bold{79}, \bold{134} + \item \isa {dvd_add} (theorem), \bold{134} \item \isa {dvd_anti_sym} (theorem), \bold{134} - \item \isa {dvd_def} (theorem), \bold{68}, \bold{78}, \bold{134} - \item \isa {dvd_mod} (theorem), \bold{87} - \item \isa {dvd_mod_imp_dvd} (theorem), \bold{86} - \item \isa {dvd_refl} (theorem), \bold{79} - \item \isa {dvd_trans} (theorem), \bold{87} + \item \isa {dvd_def} (theorem), \bold{134} \indexspace @@ -237,15 +217,10 @@ \item Euclid's algorithm, \hyperpage{85--87} \item even numbers \subitem defining inductively, \hyperpage{111--115} - \item \isa {even.cases} (theorem), \bold{114} - \item \isa {even.induct} (theorem), \bold{112} - \item \isa {even.step} (theorem), \bold{112} - \item \isa {even.zero} (theorem), \bold{112} \item \texttt {EX}, \bold{189} \item \isa {Ex} (constant), \hyperpage{93} \item \isa {exE} (theorem), \bold{66} \item \isa {exI} (theorem), \bold{66} - \item \isa {expand_fun_eq} (theorem), \bold{94} \item \isa {ext} (theorem), \bold{93} \item extensionality \subitem for functions, \bold{93, 94} @@ -267,25 +242,21 @@ \item \isa {frule} (method), \hyperpage{67} \item \isa {frule_tac} (method), \hyperpage{60} \item \isa {fst}, \bold{21} - \item \isa {fun_upd_apply} (theorem), \bold{94} - \item \isa {fun_upd_upd} (theorem), \bold{94} \item functions, \hyperpage{93--95} \indexspace \item \isa {gcd} (constant), \hyperpage{76--78}, \hyperpage{85--87} - \item \isa {gcd_mult_distrib2} (theorem), \bold{77} \item generalizing for induction, \hyperpage{113} - \item \isa {gfp_unfold} (theorem), \bold{100} \item Girard, Jean-Yves, \fnote{55} \item ground terms example, \hyperpage{119--124} - \item \isa {gterm_Apply_elim} (theorem), \bold{123} \indexspace - \item \isa {hd}, \bold{15} + \item \isa {hd} (constant), \hyperpage{15} \item higher-order pattern, \bold{159} \item Hilbert's $\varepsilon$-operator, \hyperpage{69--71} + \item {\textit {hypreal}} (type), \hyperpage{137} \indexspace @@ -303,11 +274,8 @@ \item image \subitem under a function, \bold{95} \subitem under a relation, \bold{96} - \item \isa {image_compose} (theorem), \bold{95} \item \isa {image_def} (theorem), \bold{95} \item \isa {Image_iff} (theorem), \bold{96} - \item \isa {image_Int} (theorem), \bold{95} - \item \isa {image_Un} (theorem), \bold{95} \item \isa {impI} (theorem), \bold{56} \item implication, \hyperpage{56--57} \item \isa {induct_tac}, \hyperpage{10}, \hyperpage{17}, @@ -327,13 +295,14 @@ \item inner syntax, \bold{9} \item \isa {insert} (constant), \hyperpage{91} \item \isa {insert} (method), \hyperpage{80--82} - \item \isa {insert_is_Un} (theorem), \bold{91} \item instance, \bold{145} \item \texttt {INT}, \bold{189} \item \texttt {Int}, \bold{189} + \item \isa {int} (type), \hyperpage{135} \item \isa {INT_iff} (theorem), \bold{92} \item \isa {IntD1} (theorem), \bold{89} \item \isa {IntD2} (theorem), \bold{89} + \item integers, \hyperpage{135} \item \isa {INTER} (constant), \hyperpage{93} \item \texttt {Inter}, \bold{189} \item \isa {Inter_iff} (theorem), \bold{92} @@ -344,10 +313,7 @@ \item \isa {intro!} (attribute), \hyperpage{112} \item introduction rules, \hyperpage{52--53} \item \isa {inv} (constant), \hyperpage{70} - \item \isa {inv_def} (theorem), \bold{70} - \item \isa {inv_f_f} (theorem), \bold{94} \item \isa {inv_image_def} (theorem), \bold{99} - \item \isa {inv_inv_eq} (theorem), \bold{94} \item inverse \subitem of a function, \bold{94} \subitem of a relation, \bold{96} @@ -357,17 +323,16 @@ \indexspace - \item \isa {kill}, \bold{14} + \item \isacommand {kill} (command), \hyperpage{14} \indexspace - \item \isa {le_less_trans} (theorem), \bold{171} - \item \isa {LEAST}, \bold{20} + \item \isa {LEAST}, \bold{21} \item least number operator, \hyperpage{69} \item lemma, \hyperpage{11} \item \isa {lemma}, \bold{11} \item \isacommand {lemmas} (command), \hyperpage{77}, \hyperpage{86} - \item \isa {length}, \bold{15} + \item \isa {length} (symbol), \hyperpage{15} \item \isa {length_induct}, \bold{172} \item \isa {less_than} (constant), \hyperpage{98} \item \isa {less_than_iff} (theorem), \bold{98} @@ -376,11 +341,8 @@ \item lexicographic product, \bold{99}, \hyperpage{160} \item {\texttt{lfp}} \subitem applications of, \see{CTL}{100} - \item \isa {lfp_induct} (theorem), \bold{100} - \item \isa {lfp_unfold} (theorem), \bold{100} - \item linear arithmetic, \bold{21} + \item linear arithmetic, \bold{21}, \hyperpage{131} \item \isa {list}, \hyperpage{2}, \bold{7}, \bold{15} - \item \isa {lists_Int_eq} (theorem), \bold{123} \item \isa {lists_mono} (theorem), \bold{121} \indexspace @@ -390,64 +352,52 @@ \item \isa {max}, \bold{20, 21} \item measure function, \bold{45}, \bold{98} \item \isa {measure_def} (theorem), \bold{99} - \item \isa {mem_Collect_eq} (theorem), \bold{91} \item meta-logic, \bold{64} - \item method, \bold{14} + \item methods, \bold{14} \item \isa {min}, \bold{20, 21} \item \isa {mod}, \bold{20} - \item \isa {mod_div_equality} (theorem), \bold{81}, \bold{133} - \item \isa {mod_if} (theorem), \bold{133} - \item \isa {mod_mult1_eq} (theorem), \bold{133} - \item \isa {mod_mult2_eq} (theorem), \bold{133} + \item \isa {mod_div_equality} (theorem), \bold{133} \item \isa {mod_mult_distrib} (theorem), \bold{133} - \item \isa {mod_Suc} (theorem), \bold{80} \item \emph{modus ponens}, \hyperpage{51}, \hyperpage{56} \item \isa {mono_def} (theorem), \bold{100} - \item \isa {mono_Int} (theorem), \bold{123} - \item \isa {monoD} (theorem), \bold{100} - \item \isa {monoI} (theorem), \bold{100} \item monotone functions, \bold{100}, \hyperpage{123} \subitem and inductive definitions, \hyperpage{121--122} \item \isa {mp} (theorem), \bold{56} - \item \isa {mult_commute} (theorem), \bold{61} - \item \isa {mult_le_mono} (theorem), \bold{133} - \item \isa {mult_le_mono1} (theorem), \bold{80} - \item \isa {mult_less_mono1} (theorem), \bold{133} \item multiset ordering, \bold{99} \indexspace - \item \isa {n_subsets} (theorem), \bold{93} - \item \isa {nat}, \hyperpage{2}, \bold{20} - \item \isa {nat_diff_split} (theorem), \bold{134} + \item \isa {nat}, \hyperpage{2} + \item \isa {nat} (type), \hyperpage{133--134} + \item {\textit {nat}} (type), \hyperpage{20} \item natural deduction, \hyperpage{51--52} - \item \isa {neg_mod_bound} (theorem), \bold{135} - \item \isa {neg_mod_sign} (theorem), \bold{135} + \item natural numbers, \hyperpage{133--134} \item negation, \hyperpage{57--59} \item \isa {Nil}, \bold{7} \item \isa {no_asm}, \bold{27} \item \isa {no_asm_simp}, \bold{27} \item \isa {no_asm_use}, \bold{28} + \item non-standard reals, \hyperpage{137} \item \isa {None}, \bold{22} \item \isa {notE} (theorem), \bold{57} \item \isa {notI} (theorem), \bold{57} - \item \isa {numeral_0_eq_0} (theorem), \bold{133} - \item \isa {numeral_1_eq_1} (theorem), \bold{133} + \item numeric literals, \hyperpage{132} + \subitem for type \protect\isa{nat}, \hyperpage{133} + \subitem for type \protect\isa{real}, \hyperpage{136} \indexspace \item \isa {O} (symbol), \hyperpage{96} \item \texttt {o}, \bold{189} - \item \isa {o_assoc} (theorem), \bold{94} \item \isa {o_def} (theorem), \bold{94} \item \isa {OF} (attribute), \hyperpage{78--79} \item \isa {of} (attribute), \hyperpage{77}, \hyperpage{79} \item \isa {oops}, \bold{11} \item \isa {option}, \bold{22} - \item \isa {order_antisym} (theorem), \bold{69} \item ordered rewriting, \bold{158} \item outer syntax, \bold{9} \item overloading, \hyperpage{144--146} + \subitem and arithmetic, \hyperpage{132} \indexspace @@ -457,12 +407,8 @@ \item pattern, higher-order, \bold{159} \item PDL, \hyperpage{102--105} \item permutative rewrite rule, \bold{158} - \item \isa {pos_mod_bound} (theorem), \bold{135} - \item \isa {pos_mod_sign} (theorem), \bold{135} - \item \isa {pr}, \bold{14} - \item \isacommand {pr} (command), \hyperpage{83} - \item \isa {prefer}, \bold{14} - \item \isacommand {prefer} (command), \hyperpage{84} + \item \isacommand {pr} (command), \hyperpage{14}, \hyperpage{83} + \item \isacommand {prefer} (command), \hyperpage{14}, \hyperpage{84} \item primitive recursion, \bold{16} \item \isa {primrec}, \hyperpage{8}, \bold{16}, \hyperpage{36--42} \item product type, \see{pair}{1} @@ -485,33 +431,26 @@ \item \isa {r_into_rtrancl} (theorem), \bold{96} \item \isa {r_into_trancl} (theorem), \bold{97} - \item \isa {R_O_Id} (theorem), \bold{96} \item range \subitem of a function, \hyperpage{95} \subitem of a relation, \hyperpage{96} \item \isa {range} (symbol), \hyperpage{95} \item \isa {Range_iff} (theorem), \bold{96} - \item \isa {real_add_divide_distrib} (theorem), \bold{136} - \item \isa {real_dense} (theorem), \bold{136} - \item \isa {real_divide_divide1_eq} (theorem), \bold{136} - \item \isa {real_divide_divide2_eq} (theorem), \bold{136} - \item \isa {real_divide_minus_eq} (theorem), \bold{136} - \item \isa {real_minus_divide_eq} (theorem), \bold{136} - \item \isa {real_times_divide1_eq} (theorem), \bold{136} - \item \isa {real_times_divide2_eq} (theorem), \bold{136} - \item \isa {realpow_abs} (theorem), \bold{136} + \item \isa {real} (type), \hyperpage{136--137} + \item real numbers, \hyperpage{136--137} \item \isa {recdef}, \hyperpage{45--50}, \hyperpage{160--168} \item \isacommand {recdef} (command), \hyperpage{98} + \item \protect\isacommand{recdef} (command) + \subitem and numeric literals, \hyperpage{132} \item \isa {recdef_cong}, \bold{164} \item \isa {recdef_simp}, \bold{47} \item \isa {recdef_wf}, \bold{162} \item recursion \subitem well-founded, \bold{161} \item recursion induction, \hyperpage{49--50} - \item \isa {redo}, \bold{14} + \item \isacommand {redo} (command), \hyperpage{14} \item relations, \hyperpage{95--98} \subitem well-founded, \hyperpage{98--99} - \item \isa {relprime_dvd_mult} (theorem), \bold{78} \item \isa {rename_tac} (method), \hyperpage{66--67} \item \isa {rev}, \bold{8} \item rewrite rule, \bold{26} @@ -519,11 +458,8 @@ \item rewriting, \bold{26} \subitem ordered, \bold{158} \item \isa {rotate_tac}, \bold{28} - \item \isa {rtrancl_idemp} (theorem), \bold{97} - \item \isa {rtrancl_induct} (theorem), \bold{97} \item \isa {rtrancl_refl} (theorem), \bold{96} \item \isa {rtrancl_trans} (theorem), \bold{96} - \item \isa {rtrancl_unfold} (theorem), \bold{96} \item rule induction, \hyperpage{112--114} \item rule inversion, \hyperpage{114--115}, \hyperpage{123--124} \item \isa {rule_tac} (method), \hyperpage{60} @@ -555,15 +491,15 @@ \item simplification rule, \bold{26}, \hyperpage{159--160} \item \isa {simplified} (attribute), \hyperpage{77}, \hyperpage{79} \item simplifier, \bold{25} - \item \isa {size}, \bold{15} + \item \isa {size} (constant), \hyperpage{15} \item \isa {snd}, \bold{21} \item \isa {SOME} (symbol), \hyperpage{69} \item \texttt {SOME}, \bold{189} \item \isa {Some}, \bold{22} \item \isa {some_equality} (theorem), \bold{69} - \item \isa {someI} (theorem), \bold{70}, \bold{75} + \item \isa {someI} (theorem), \bold{70} \item \isa {someI2} (theorem), \bold{70} - \item \isa {someI_ex} (theorem, \bold){71} + \item \isa {someI_ex} (theorem), \bold{71} \item sort, \bold{150} \item \isa {spec} (theorem), \bold{64} \item \isa {split} (constant), \bold{137} @@ -578,11 +514,8 @@ \item \isa {subsetI} (theorem), \bold{90} \item \isa {subst} (method), \hyperpage{61} \item substitution, \hyperpage{61--63} - \item \isa {Suc}, \bold{20} - \item \isa {Suc_leI} (theorem), \bold{171} - \item \isa {Suc_Suc_cases} (theorem), \bold{115} + \item \isa {Suc} (constant), \hyperpage{20} \item \isa {surj_def} (theorem), \bold{94} - \item \isa {surj_f_inv_f} (theorem), \bold{94} \item surjections, \hyperpage{94} \item \isa {sym} (theorem), \bold{77} \item syntax translation, \bold{23} @@ -592,7 +525,7 @@ \item tactic, \bold{10} \item tacticals, \hyperpage{82--83} \item term, \bold{3} - \item \isa {term}, \bold{14} + \item \isacommand {term} (command), \hyperpage{14} \item term rewriting, \bold{26} \item termination, \see{total function}{1} \item \isa {THEN} (attribute), \bold{77}, \hyperpage{79}, @@ -602,17 +535,16 @@ \item theory, \bold{2} \subitem abandon, \bold{14} \item theory file, \bold{2} - \item \isa {thm}, \bold{14} - \item \isa {tl}, \bold{15} + \item \isacommand {thm} (command), \hyperpage{14} + \item \isa {tl} (constant), \hyperpage{15} \item total function, \hyperpage{9} \item \isa {trace_simp}, \bold{31} \item tracing the simplifier, \bold{31} - \item \isa {trancl_converse} (theorem), \bold{97} \item \isa {trancl_trans} (theorem), \bold{97} - \item \isa {translations}, \bold{23} + \item \isa {translations}, \bold{24} \item \isa {True}, \bold{3} \item tuple, \see{pair}{1} - \item \isa {typ}, \bold{14} + \item \isacommand {typ} (command), \hyperpage{14} \item type, \bold{2} \item type constraint, \bold{4} \item type declaration, \bold{150} @@ -622,7 +554,7 @@ \item type variable, \bold{3} \item \isa {typedecl}, \bold{151} \item \isa {typedef}, \bold{151} - \item \isa {types}, \bold{22} + \item \isa {types}, \bold{23} \indexspace @@ -633,7 +565,7 @@ \item \isa {UN_iff} (theorem), \bold{92} \item \isa {Un_subset_iff} (theorem), \bold{90} \item underdefined function, \hyperpage{165} - \item \isa {undo}, \bold{14} + \item \isacommand {undo} (command), \hyperpage{14} \item \isa {unfold}, \bold{28} \item unification, \hyperpage{60--63} \item \isa {UNION} (constant), \hyperpage{93} @@ -652,25 +584,11 @@ \item variable, \bold{4} \subitem schematic, \bold{4} \subitem type, \bold{3} - \item \isa {vimage_Compl} (theorem), \bold{95} \item \isa {vimage_def} (theorem), \bold{95} \indexspace \item \isa {wf_induct} (theorem), \bold{99} - \item \isa {wf_inv_image} (theorem), \bold{99} - \item \isa {wf_less_than} (theorem), \bold{98} - \item \isa {wf_lex_prod} (theorem), \bold{99} - \item \isa {wf_measure} (theorem), \bold{99} \item \isa {while}, \bold{167} - \indexspace - - \item \isa {zdiv_zadd1_eq} (theorem), \bold{135} - \item \isa {zdiv_zmult1_eq} (theorem), \bold{135} - \item \isa {zdiv_zmult2_eq} (theorem), \bold{135} - \item \isa {zmod_zadd1_eq} (theorem), \bold{135} - \item \isa {zmod_zmult1_eq} (theorem), \bold{135} - \item \isa {zmod_zmult2_eq} (theorem), \bold{135} - \end{theindex}