doc-src/TutorialI/IsarOverview/Isar/Logic.thy
changeset 13313 e4dc78f4e51e
parent 13312 ad91cf279f06
child 13317 bb74918cc0dd
equal deleted inserted replaced
13312:ad91cf279f06 13313:e4dc78f4e51e
   697   proof induct
   697   proof induct
   698     fix x assume "(x,z) \<in> r*"  -- {*@{text B}[@{text y} := @{text x}]*}
   698     fix x assume "(x,z) \<in> r*"  -- {*@{text B}[@{text y} := @{text x}]*}
   699     thus "(x,z) \<in> r*" .
   699     thus "(x,z) \<in> r*" .
   700   next
   700   next
   701     fix x' x y
   701     fix x' x y
   702     assume step: "(x',x) \<in> r" and
   702     assume 1: "(x',x) \<in> r" and
   703            IH: "(y,z) \<in> r* \<Longrightarrow> (x,z) \<in> r*" and
   703            IH: "(y,z) \<in> r* \<Longrightarrow> (x,z) \<in> r*" and
   704            B:  "(y,z) \<in> r*"
   704            B:  "(y,z) \<in> r*"
   705     from step IH[OF B] show "(x',z) \<in> r*" by(rule rtc.step)
   705     from 1 IH[OF B] show "(x',z) \<in> r*" by(rule rtc.step)
   706   qed
   706   qed
   707 qed
   707 qed
   708 
   708 
   709 text{*\noindent We start the proof with \isakeyword{from}~@{text"A
   709 text{*\noindent We start the proof with \isakeyword{from}~@{text"A
   710 B"}. Only @{text A} is ``consumed'' by the first proof step, here
   710 B"}. Only @{text A} is ``consumed'' by the first proof step, here