diff -r a80d8ec6c998 -r 3dda49e08b9d src/Doc/Isar_Ref/First_Order_Logic.thy --- a/src/Doc/Isar_Ref/First_Order_Logic.thy Fri Jan 04 21:49:06 2019 +0100 +++ b/src/Doc/Isar_Ref/First_Order_Logic.thy Fri Jan 04 23:22:53 2019 +0100 @@ -20,8 +20,8 @@ text \ Note that the object-logic judgment is implicit in the syntax: writing - @{prop A} produces @{term "Trueprop A"} internally. From the Pure - perspective this means ``@{prop A} is derivable in the object-logic''. + \<^prop>\A\ produces \<^term>\Trueprop A\ internally. From the Pure + perspective this means ``\<^prop>\A\ is derivable in the object-logic''. \ @@ -41,7 +41,7 @@ text \ Substitution is very powerful, but also hard to control in full generality. - We derive some common symmetry~/ transitivity schemes of @{term equal} as + We derive some common symmetry~/ transitivity schemes of \<^term>\equal\ as particular consequences. \ @@ -182,10 +182,9 @@ and conjD\<^sub>2: "A \ B \ B" text \ - The conjunctive destructions have the disadvantage that decomposing @{prop - "A \ B"} involves an immediate decision which component should be projected. - The more convenient simultaneous elimination @{prop "A \ B \ (A \ B \ C) \ - C"} can be derived as follows: + The conjunctive destructions have the disadvantage that decomposing \<^prop>\A \ B\ involves an immediate decision which component should be projected. + The more convenient simultaneous elimination \<^prop>\A \ B \ (A \ B \ C) \ + C\ can be derived as follows: \ theorem conjE [elim]: @@ -300,8 +299,8 @@ These examples illustrate both classical reasoning and non-trivial propositional proofs in general. All three rules characterize classical logic independently, but the original rule is already the most convenient to - use, because it leaves the conclusion unchanged. Note that @{prop "(\ C \ C) - \ C"} fits again into our format for eliminations, despite the additional + use, because it leaves the conclusion unchanged. Note that \<^prop>\(\ C \ C) + \ C\ fits again into our format for eliminations, despite the additional twist that the context refers to the main conclusion. So we may write @{thm classical} as the Isar statement ``\<^theory_text>\obtains \ thesis\''. This also explains nicely how classical reasoning really works: whatever the main \thesis\ @@ -317,7 +316,7 @@ Representing quantifiers is easy, thanks to the higher-order nature of the underlying framework. According to the well-known technique introduced by Church @{cite "church40"}, quantifiers are operators on predicates, which - are syntactically represented as \\\-terms of type @{typ "i \ o"}. Binder + are syntactically represented as \\\-terms of type \<^typ>\i \ o\. Binder notation turns \All (\x. B x)\ into \\x. B x\ etc. \