--- a/doc-src/TutorialI/Sets/Recur.thy Tue Aug 28 18:46:15 2012 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,80 +0,0 @@
-theory Recur imports Main begin
-
-
-text{*
-@{thm[display] mono_def[no_vars]}
-\rulename{mono_def}
-
-@{thm[display] monoI[no_vars]}
-\rulename{monoI}
-
-@{thm[display] monoD[no_vars]}
-\rulename{monoD}
-
-@{thm[display] lfp_unfold[no_vars]}
-\rulename{lfp_unfold}
-
-@{thm[display] lfp_induct[no_vars]}
-\rulename{lfp_induct}
-
-@{thm[display] gfp_unfold[no_vars]}
-\rulename{gfp_unfold}
-
-@{thm[display] coinduct[no_vars]}
-\rulename{coinduct}
-*}
-
-text{*\noindent
-A relation $<$ is
-\bfindex{wellfounded} if it has no infinite descending chain $\cdots <
-a@2 < a@1 < a@0$. Clearly, a function definition is total iff the set
-of all pairs $(r,l)$, where $l$ is the argument on the left-hand side
-of an equation and $r$ the argument of some recursive call on the
-corresponding right-hand side, induces a wellfounded relation.
-
-The HOL library formalizes
-some of the theory of wellfounded relations. For example
-@{prop"wf r"}\index{*wf|bold} means that relation @{term[show_types]"r::('a*'a)set"} is
-wellfounded.
-Finally we should mention that HOL already provides the mother of all
-inductions, \textbf{wellfounded
-induction}\indexbold{induction!wellfounded}\index{wellfounded
-induction|see{induction, wellfounded}} (@{thm[source]wf_induct}):
-@{thm[display]wf_induct[no_vars]}
-where @{term"wf r"} means that the relation @{term r} is wellfounded
-
-*}
-
-text{*
-
-@{thm[display] wf_induct[no_vars]}
-\rulename{wf_induct}
-
-@{thm[display] less_than_iff[no_vars]}
-\rulename{less_than_iff}
-
-@{thm[display] inv_image_def[no_vars]}
-\rulename{inv_image_def}
-
-@{thm[display] measure_def[no_vars]}
-\rulename{measure_def}
-
-@{thm[display] wf_less_than[no_vars]}
-\rulename{wf_less_than}
-
-@{thm[display] wf_inv_image[no_vars]}
-\rulename{wf_inv_image}
-
-@{thm[display] wf_measure[no_vars]}
-\rulename{wf_measure}
-
-@{thm[display] lex_prod_def[no_vars]}
-\rulename{lex_prod_def}
-
-@{thm[display] wf_lex_prod[no_vars]}
-\rulename{wf_lex_prod}
-
-*}
-
-end
-