--- a/doc-src/IsarRef/Thy/Proof.thy Fri Jul 01 19:57:41 2011 +0200
+++ b/doc-src/IsarRef/Thy/Proof.thy Fri Jul 01 22:48:05 2011 +0200
@@ -1366,11 +1366,12 @@
The optional ``@{text "arbitrary: x\<^sub>1 \<dots> x\<^sub>m"}''
specification generalizes variables @{text "x\<^sub>1, \<dots>,
- x\<^sub>m"} of the original goal before applying induction. Thus
- induction hypotheses may become sufficiently general to get the
- proof through. Together with definitional instantiations, one may
- effectively perform induction over expressions of a certain
- structure.
+ x\<^sub>m"} of the original goal before applying induction. One can
+ separate variables by ``@{text "and"}'' to generalize them in other
+ goals then the first. Thus induction hypotheses may become
+ sufficiently general to get the proof through. Together with
+ definitional instantiations, one may effectively perform induction
+ over expressions of a certain structure.
The optional ``@{text "taking: t\<^sub>1 \<dots> t\<^sub>n"}''
specification provides additional instantiations of a prefix of
--- a/doc-src/IsarRef/Thy/document/Proof.tex Fri Jul 01 19:57:41 2011 +0200
+++ b/doc-src/IsarRef/Thy/document/Proof.tex Fri Jul 01 22:48:05 2011 +0200
@@ -1898,11 +1898,12 @@
using the \indexdef{}{attribute}{induct\_simp}\hypertarget{attribute.induct-simp}{\hyperlink{attribute.induct-simp}{\mbox{\isa{induct{\isaliteral{5F}{\isacharunderscore}}simp}}}} attribute.
The optional ``\isa{{\isaliteral{22}{\isachardoublequote}}arbitrary{\isaliteral{3A}{\isacharcolon}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}}''
- specification generalizes variables \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} of the original goal before applying induction. Thus
- induction hypotheses may become sufficiently general to get the
- proof through. Together with definitional instantiations, one may
- effectively perform induction over expressions of a certain
- structure.
+ specification generalizes variables \isa{{\isaliteral{22}{\isachardoublequote}}x\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}{\isaliteral{2C}{\isacharcomma}}\ x\isaliteral{5C3C5E7375623E}{}\isactrlsub m{\isaliteral{22}{\isachardoublequote}}} of the original goal before applying induction. One can
+ separate variables by ``\isa{{\isaliteral{22}{\isachardoublequote}}and{\isaliteral{22}{\isachardoublequote}}}'' to generalize them in other
+ goals then the first. Thus induction hypotheses may become
+ sufficiently general to get the proof through. Together with
+ definitional instantiations, one may effectively perform induction
+ over expressions of a certain structure.
The optional ``\isa{{\isaliteral{22}{\isachardoublequote}}taking{\isaliteral{3A}{\isacharcolon}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub {\isadigit{1}}\ {\isaliteral{5C3C646F74733E}{\isasymdots}}\ t\isaliteral{5C3C5E7375623E}{}\isactrlsub n{\isaliteral{22}{\isachardoublequote}}}''
specification provides additional instantiations of a prefix of