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Quelle Quick_Reference.thySprache: Isabelle |
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(*:maxLineLen=78:*) theory Quick_Reference imports Main Base begin chapter ‹Isabelle/Isar quick reference \label{ap:refcard}› section ‹Proof commands› subsection ‹Main grammar \label{ap:main-grammar}› text ‹ \begin{tabular}{rcl} ‹main› & = & 🚫‹notepad begin "statement*" end› \\ & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & & \quad🚫‹fixes vars› \\ & & \quad🚫‹assumes name: props› \\ & & \quad🚫‹shows name: props "proof"› \\ & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & & \quad🚫‹fixes vars› \\ & & \quad🚫‹assumes name: props› \\ & & \quad🚫‹obtains (name) vars where props | … "proof"› \\ ‹proof› & = & 🚫‹"refinement*" proper_proof› \\ ‹refinement› & = & 🚫‹apply method› \\ & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo ‹proper_proof› & = & 🚫‹proof "method?" "statement*" qed "method?"› \\ & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo ‹statement› & = & 🚫‹{ "statement*" }› \\ & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo ‹goal› & = & 🚫‹have name: props if name: props for vars "proof"› \\ & ‹|› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbo \end{tabular} › subsection ‹Primitives› text ‹ \begin{tabular}{ll} 🚫‹fix x› & augment context by ‹∧x. ◻› \\ 🚫‹assume a: A› & augment context by ‹A ==> ◻› \\ 🚫‹then› & indicate forward chaining of facts \\ 🚫‹have a: A› & prove local result \\ \<^theory_text>\<open>show a: A\<close> & prove local result, refining some goal \\ \<^theory_text>\<open>using a\<close> & indicate use of additional facts \\ \<^theory_text>\<open>unfolding a\<close> & unfold definitional equations \\ \<^theory_text>\<open>proof m\<^sub>1 \<dots> qed m\<^sub>2\<close> & indicate proof structure a \<^theory_text>\<open>{ \<dots> }\<close> & indicate explicit blocks \\ \<^theory_text>\<open>next\<close> & switch proof blocks \\ \<^theory_text>\<open>note a = b\<close> & reconsider and declare facts \\ \<^theory_text>\<open>let p = t\<close> & abbreviate terms by higher-order matching \\ \<^theory_text>\<open>write c (mx)\<close> & declare local mixfix syntax \\ \end{tabular} \<close> subsection \<open>Abbreviations and synonyms\<close> text \<open> \begin{tabular}{rcl} \<^theory_text>\<open>by m\<^sub>1 m\<^sub>2\<close> & \<open>\<equiv>\<close> & \<^theory_te \<^theory_text>\<open>..\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>by stand \<^theory_text>\<open>.\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>by this\<c \<^theory_text>\<open>from a\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>note \<^theory_text>\<open>with a\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>from \<^theory_text>\<open>from this\<close> & \<open>\<equiv>\<close> & \<^theory_text>\<open>t \end{tabular} \<close> subsection \<open>Derived elements\<close> text \<open> \begin{tabular}{rcl} \<^theory_text>\<open>also"\<^sub>0"\<close> & \<open>\<approx>\<close> & \<^theory_text>\< \<^theory_text>\<open>also"\<^sub>n\<^sub>+\<^sub>1"\<close> & \<open>\<approx>\<close> & \<^ \<^theory_text>\<open>finally\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>a \<^theory_text>\<open>moreover\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open> \<^theory_text>\<open>ultimately\<close> & \<open>\<approx>\<close> & \<^theory_text>\<op \<^theory_text>\<open>presume a: A\<close> & \<open>\<approx>\<close> & \<^theory_text>\<op \<^theory_text>\<open>define x where "x = t"\<close> & \<open>\<approx>\<close> & \<^theory_ \<^theory_text>\<open>consider x where A | \<dots>\<close> & \<open>\<approx>\<close> & \<^the & & \quad \<^theory_text>\<open>if "\<And>x. A \<Longrightarrow> thesis" and \<dots> for th \<^theory_text>\<open>obtain x where a: A \<proof>\<close> & \<open>\<approx>\<close> & \<^the & & \<^theory_text>\<open>fix x assume a: A\<close> \\ \<^theory_text>\<open>case c\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>fix \<^theory_text>\<open>sorry\<close> & \<open>\<approx>\<close> & \<^theory_text>\<open>by c \end{tabular} \<close> subsection \<open>Diagnostic commands\<close> text \<open> \begin{tabular}{ll} \<^theory_text>\<open>typ \<tau>\<close> & print type \\ \<^theory_text>\<open>term t\<close> & print term \\ \<^theory_text>\<open>prop \<phi>\<close> & print proposition \\ \<^theory_text>\<open>thm a\<close> & print fact \\ \<^theory_text>\<open>print_statement a\<close> & print fact in long statement form \\ \end{tabular} \<close> section \<open>Proof methods\<close> text \<open> \begin{tabular}{ll} \multicolumn{2}{l}{\<^bold>\<open>Single steps (forward-chaining facts)\<close>} \\[0.5ex] @{method assumption} & apply some goal assumption \\ @{method this} & apply current facts \\ @{method rule}~\<open>a\<close> & apply some rule \\ @{method standard} & apply standard rule (default for @{command "proof"}) \\ @{method contradiction} & apply \<open>\<not>\<close> elimination rule (any order) \\ @{method cases}~\<open>t\<close> & case analysis (provides cases) \\ @{method induct}~\<open>x\<close> & proof by induction (provides cases) \\[2ex] \multicolumn{2}{l}{\<^bold>\<open>Repeated steps (inserting facts)\<close>} \\[0.5ex] @{method "-"} & no rules \\ @{method intro}~\<open>a\<close> & introduction rules \\ @{method intro_classes} & class introduction rules \\ @{method intro_locales} & locale introduction rules (without body) \\ @{method unfold_locales} & locale introduction rules (with body) \\ @{method elim}~\<open>a\<close> & elimination rules \\ @{method unfold}~\<open>a\<close> & definitional rewrite rules \\[2ex] \multicolumn{2}{l}{\<^bold>\<open>Automated proof tools (inserting facts)\<close>} \\[0.5ex @{method iprover} & intuitionistic proof search \\ @{method blast}, @{method fast} & Classical Reasoner \\ @{method simp}, @{method simp_all} & Simplifier (+ Splitter) \\ @{method auto}, @{method force} & Simplifier + Classical Reasoner \\ @{method arith} & Arithmetic procedures \\ \end{tabular} \<close> section \<open>Attributes\<close> text \<open> \begin{tabular}{ll} \multicolumn{2}{l}{\<^bold>\<open>Rules\<close>} \\[0.5ex] @{attribute OF}~\<open>a\<close> & rule resolved with facts (skipping ``\<open>_\<close>'') @{attribute of}~\<open>t\<close> & rule instantiated with terms (skipping ``\<open>_\<clos @{attribute "where"}~\<open>x = t\<close> & rule instantiated with terms, by variable name @{attribute symmetric} & resolution with symmetry rule \\ @{attribute THEN}~\<open>b\<close> & resolution with another rule \\ @{attribute rule_format} & result put into standard rule format \\ @{attribute elim_format} & destruct rule turned into elimination rule format \\[1ex] \multicolumn{2}{l}{\<^bold>\<open>Declarations\<close>} \\[0.5ex] @{attribute simp} & Simplifier rule \\ @{attribute intro}, @{attribute elim}, @{attribute dest} & Pure or Classical Reasoner @{attribute iff} & Simplifier + Classical Reasoner rule \\ @{attribute split} & case split rule \\ @{attribute trans} & transitivity rule \\ @{attribute sym} & symmetry rule \\ \end{tabular} \<close> section \<open>Rule declarations and methods\<close> text \<open> \begin{tabular}{l|lllll} & @{method rule} & @{method iprover} & @{method blast} & @{method simp} &< & & & @{method fast} & @{method simp_all} & @{method force} \\ \hline @{attribute Pure.elim}\<open>!\<close> @{attribute Pure.intro}\<open>!\<close> & \<open>\<times>\<close> & \<open>\<times>\<close> \\ @{attribute Pure.elim} @{attribute Pure.intro} & \<open>\<times>\<close> & \<open>\<times>\<close> \\ @{attribute elim}\<open>!\<close> @{attribute intro}\<open>!\<close> & \<open>\<times>\<close> & & \<open>\<times>\<close> & & \<open>\<times>\<clos @{attribute elim} @{attribute intro} & \<open>\<times>\<close> & & \<open>\<times>\<close> & & \<open>\<times>\<clos @{attribute iff} & \<open>\<times>\<close> & & \<open>\<times>\<close> & \<open>\<times>\<close> &> \<open>\<times>\<close> \\ @{attribute iff}\<open>?\<close> & \<open>\<times>\<close> \\ @{attribute elim}\<open>?\<close> @{attribute intro}\<open>?\<close> & \<open>\<times>\<close> \\ @{attribute simp} & & & & \<open>\<times>\<close> & \<open>\<times>\<close> \\ @{attribute cong} & & & & \<open>\<times>\<close> & \<open>\<times>\<close> \\ @{attribute split} & & & & \<open>\<times>\<close> & \<open>\<times>\<close> \\ \end{tabular} \<close> section \<open>Proof scripts\<close> subsection \<open>Commands\<close> text \<open> \begin{tabular}{ll} \<^theory_text>\<open>apply m\<close> & apply proof method during backwards refinement \\ \<^theory_text>\<open>apply_end m\<close> & apply proof method (as if in terminal position) \<^theory_text>\<open>supply a\<close> & supply facts during backwards refinement \\ \<^theory_text>\<open>subgoal\<close> & nested proof during backwards refinement \\ \<^theory_text>\<open>defer n\<close> & move subgoal to end \\ \<^theory_text>\<open>prefer n\<close> & move subgoal to start \\ \<^theory_text>\<open>back\<close> & backtrack last command \\ \<^theory_text>\<open>done\<close> & complete proof \\ \end{tabular} \<close> subsection \<open>Methods\<close> text \<open> \begin{tabular}{ll} @{method rule_tac}~\<open>insts\<close> & resolution (with instantiation) \\ @{method erule_tac}~\<open>insts\<close> & elim-resolution (with instantiation) \\ @{method drule_tac}~\<open>insts\<close> & destruct-resolution (with instantiation) \ @{method frule_tac}~\<open>insts\<close> & forward-resolution (with instantiation) \\ @{method cut_tac}~\<open>insts\<close> & insert facts (with instantiation) \\ @{method thin_tac}~\<open>\<phi>\<close> & delete assumptions \\ @{method subgoal_tac}~\<open>\<phi>\<close> & new claims \\ @{method rename_tac}~\<open>x\<close> & rename innermost goal parameters \\ @{method rotate_tac}~\<open>n\<close> & rotate assumptions of goal \\ @{method tactic}~\<open>text\<close> & arbitrary ML tactic \\ @{method case_tac}~\<open>t\<close> & exhaustion (datatypes) \\ @{method induct_tac}~\<open>x\<close> & induction (datatypes) \\ @{method ind_cases}~\<open>t\<close> & exhaustion + simplification (inductive predicat \end{tabular} \<close> end
¤ Dauer der Verarbeitung: 0.20 Sekunden (vorverarbeitet am 2026-08-25) ¤*© Formatika GbR, Deutschland |
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2026-08-25