(*:maxLineLen=78:*) theory Quick_Referenceimports Main Basebegin 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* › \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ theorem name: props if name: props for vars "proof"› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ theorem name:› \\ \quad 🚫 ‹ fixes vars› \\ \quad 🚫 ‹ assumes name: props› \\ \quad 🚫 ‹ shows name: props "proof"› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ theorem name:› \\ \quad 🚫 ‹ fixes vars› \\ \quad 🚫 ‹ assumes name: props› \\ \quad 🚫 ‹ obtains (name) vars where props | … "proof"› \\ ‹ proof› & = & 🚫 ‹ "refinement* › \\ ‹ refinement› & = & 🚫 ‹ apply method› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ supply name = thms› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ subgoal premises name for vars "proof"› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ using thms› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ unfolding thms› \\ ‹ proper_proof› & = & 🚫 ‹ proof "method? * ? › \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ done› \\ ‹ statement› & = & 🚫 ‹ { "statement* › \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ next› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ note name = thms› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ let "term" = "term"› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ write name (mixfix)› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ fix vars› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ assume name: props if props for vars› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ then"? › \\ ‹ goal› & = & 🚫 ‹ have name: props if name: props for vars "proof"› \\ ‹ |› & ='alert("unbekanntes Symbol theory_text");' ontouchend='alert("unbekanntes Symbol theory_text");' >🚫 ‹ show name: props if name: props for vars "proof"› \\ \end {tabular}› subsection ‹ Primitives› text ‹ \begin {tabular}{ll}🚫 ‹ fix x› & augment context by ‹ ∧ ◻ › \\ 🚫 ‹ 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 and refinements \ \ \ < ^ 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_text > \ < open > proof m \ < ^ sub > 1 qed m \ < ^ sub > 2 \ < close > \ \ \ < ^ theory_text > \ < open > . . \ < close > & \ < open > \ < equiv > \ < close > & \ < ^ theory_text > \ < open > by standard \ < close > \ \ \ < ^ theory_text > \ < open > . \ < close > & \ < open > \ < equiv > \ < close > & \ < ^ theory_text > \ < open > by this \ < close > \ \ \ < ^ theory_text > \ < open > from a \ < close > & \ < open > \ < equiv > \ < close > & \ < ^ theory_text > \ < open > note a then \ < close > \ \ \ < ^ theory_text > \ < open > with a \ < close > & \ < open > \ < equiv > \ < close > & \ < ^ theory_text > \ < open > from a and this \ < close > \ \ \ < ^ theory_text > \ < open > from this \ < close > & \ < open > \ < equiv > \ < close > & \ < ^ theory_text > \ < open > then \ < close > \ \ \ 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 > \ < open > note calculation = this \ < close > \ \ \ < ^ theory_text > \ < open > also " \ < ^ sub > n \ < ^ sub > + \ < ^ sub > 1 " \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > note calculation = trans [ OF calculation this ] \ < close > \ \ \ < ^ theory_text > \ < open > finally \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > also from calculation \ < close > \ \ [ 0 . 5 ex ] \ < ^ theory_text > \ < open > moreover \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > note calculation = calculation this \ < close > \ \ \ < ^ theory_text > \ < open > ultimately \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > moreover from calculation \ < close > \ \ [ 0 . 5 ex ] \ < ^ theory_text > \ < open > presume a : A \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > assume a : A \ < close > \ \ \ < ^ theory_text > \ < open > define x where " x = t " \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > fix x assume x_def : " x = t " \ < close > \ \ \ < ^ theory_text > \ < open > consider x where A | \ < dots > \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > have thesis \ < close > \ \ & & \ quad \ < ^ theory_text > \ < open > if " \ < And > x . A \ < Longrightarrow > thesis " and \ < dots > for thesis \ < close > \ \ \ < ^ theory_text > \ < open > obtain x where a : A \ < proof > \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > consider x where A \ < proof > \ < close > \ \ & & \ < ^ theory_text > \ < open > fix x assume a : A \ < close > \ \ \ < ^ theory_text > \ < open > case c \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > fix x assume c : A \ < close > \ \ \ < ^ theory_text > \ < open > sorry \ < close > & \ < open > \ < approx > \ < close > & \ < ^ theory_text > \ < open > by cheating \ < close > \ \ \ 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 . 5 ex ] @ { 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 ) \ \ [ 2 ex ] \ multicolumn { 2 } { l } { \ < ^ bold > \ < open > Repeated steps ( inserting facts ) \ < close > } \ \ [ 0 . 5 ex ] @ { 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 \ \ [ 2 ex ] \ multicolumn { 2 } { l } { \ < ^ bold > \ < open > Automated proof tools ( inserting facts ) \ < close > } \ \ [ 0 . 5 ex ] @ { 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 . 5 ex ] @ { attribute OF } ~ \ < open > a \ < close > & rule resolved with facts ( skipping ` ` \ < open > _ \ < close > ' ' ) \ \ @ { attribute of } ~ \ < open > t \ < close > & rule instantiated with terms ( skipping ` ` \ < open > _ \ < close > ' ' ) \ \ @ { 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 \ \ [ 1 ex ] \ multicolumn { 2 } { l } { \ < ^ bold > \ < open > Declarations \ < close > } \ \ [ 0 . 5 ex ] @ { attribute simp } & Simplifier rule \ \ @ { attribute intro } , @ { attribute elim } , @ { attribute dest } & Pure or Classical Reasoner rule \ \ @ { 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 } &</span> @ { method auto } \ \ & & & @ { 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 > \ < close > \ \ @ { attribute elim } @ { attribute intro } & \ < open > \ < times > \ < close > & & \ < open > \ < times > \ < close > & & \ < open > \ < times > \ < close > \ \ @ { 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 predicates ) \ \ \ end { tabular } \ < close > end
Messung V0.5 in Prozent C=77 H=2 G=54
¤ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet am 2026-08-25)
¤ *© Formatika GbR, Deutschland
