doc-src/TutorialI/IsarOverview/Isar/Logic.thy
changeset 13312 ad91cf279f06
parent 13311 50d821437370
child 13313 e4dc78f4e51e
equal deleted inserted replaced
13311:50d821437370 13312:ad91cf279f06
   693 lemma assumes A: "(x,y) \<in> r*" and B: "(y,z) \<in> r*"
   693 lemma assumes A: "(x,y) \<in> r*" and B: "(y,z) \<in> r*"
   694   shows "(x,z) \<in> r*"
   694   shows "(x,z) \<in> r*"
   695 proof -
   695 proof -
   696   from A B show ?thesis
   696   from A B show ?thesis
   697   proof induct
   697   proof induct
   698     fix x assume "(x,z) \<in> r*"  -- "B[y := 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 step: "(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