equal
deleted
inserted
replaced
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 |