diff -r 143f58bb34f9 -r 0909deb8059b src/HOL/Algebra/FiniteProduct.thy --- a/src/HOL/Algebra/FiniteProduct.thy Thu May 26 16:57:14 2016 +0200 +++ b/src/HOL/Algebra/FiniteProduct.thy Thu May 26 17:51:22 2016 +0200 @@ -12,10 +12,10 @@ subsubsection \Inductive Definition of a Relation for Products over Sets\ -text \Instantiation of locale @{text LC} of theory @{text Finite_Set} is not +text \Instantiation of locale \LC\ of theory \Finite_Set\ is not possible, because here we have explicit typing rules like - @{text "x \ carrier G"}. We introduce an explicit argument for the domain - @{text D}.\ + \x \ carrier G\. We introduce an explicit argument for the domain + \D\.\ inductive_set foldSetD :: "['a set, 'b => 'a => 'a, 'a] => ('b set * 'a) set" @@ -111,7 +111,7 @@ apply (erule foldSetD.cases) apply blast apply clarify - txt \force simplification of @{text "card A < card (insert ...)"}.\ + txt \force simplification of \card A < card (insert ...)\.\ apply (erule rev_mp) apply (simp add: less_Suc_eq_le) apply (rule impI) @@ -221,7 +221,7 @@ ==> foldD D f e (A Un B) = foldD D f (foldD D f e B) A" by (simp add: foldD_nest_Un_Int) --- \Delete rules to do with @{text foldSetD} relation.\ +\ \Delete rules to do with \foldSetD\ relation.\ declare foldSetD_imp_finite [simp del] empty_foldSetDE [rule del] @@ -233,8 +233,8 @@ text \Commutative Monoids\ text \ - We enter a more restrictive context, with @{text "f :: 'a => 'a => 'a"} - instead of @{text "'b => 'a => 'a"}. + We enter a more restrictive context, with \f :: 'a => 'a => 'a\ + instead of \'b => 'a => 'a\. \ locale ACeD = @@ -299,7 +299,7 @@ ("(3\__\_. _)" [1000, 0, 51, 10] 10) translations "\\<^bsub>G\<^esub>i\A. b" \ "CONST finprod G (%i. b) A" - -- \Beware of argument permutation!\ + \ \Beware of argument permutation!\ lemma (in comm_monoid) finprod_empty [simp]: "finprod G f {} = \" @@ -367,7 +367,7 @@ "[| finite A; finite B; g \ A \ carrier G; g \ B \ carrier G |] ==> finprod G g (A Un B) \ finprod G g (A Int B) = finprod G g A \ finprod G g B" --- \The reversed orientation looks more natural, but LOOPS as a simprule!\ +\ \The reversed orientation looks more natural, but LOOPS as a simprule!\ proof (induct set: finite) case empty then show ?case by simp next @@ -451,7 +451,7 @@ by (rule finprod_cong') (auto simp add: simp_implies_def) text \Usually, if this rule causes a failed congruence proof error, - the reason is that the premise @{text "g \ B \ carrier G"} cannot be shown. + the reason is that the premise \g \ B \ carrier G\ cannot be shown. Adding @{thm [source] Pi_def} to the simpset is often useful. For this reason, @{thm [source] finprod_cong} is not added to the simpset by default.