# HG changeset patch # User paulson # Date 1036747709 -3600 # Node ID 0a9228532106e110243f9432e14c6e7fa22efb79 # Parent 80010ca1310c8dd031b7c88ce96d87f0299af7ce generalized wf_on_unit to wf_on_any_0 diff -r 80010ca1310c -r 0a9228532106 src/ZF/Order.thy --- a/src/ZF/Order.thy Thu Nov 07 12:35:34 2002 +0100 +++ b/src/ZF/Order.thy Fri Nov 08 10:28:29 2002 +0100 @@ -168,7 +168,11 @@ subsection{*Empty and Unit Domains*} -(** Relations over the Empty Set **) +(*The empty relation is well-founded*) +lemma wf_on_any_0: "wf[A](0)" +by (simp add: wf_on_def wf_def, fast) + +subsubsection{*Relations over the Empty Set*} lemma irrefl_0: "irrefl(0,r)" by (unfold irrefl_def, blast) @@ -198,17 +202,16 @@ done -(** The unit set is well-ordered by the empty relation (Grabczewski) **) +subsubsection{*The Empty Relation Well-Orders the Unit Set*} + +text{*by Grabczewski*} lemma tot_ord_unit: "tot_ord({a},0)" by (simp add: irrefl_def trans_on_def part_ord_def linear_def tot_ord_def) -lemma wf_on_unit: "wf[{a}](0)" -by (simp add: wf_on_def wf_def, fast) - lemma well_ord_unit: "well_ord({a},0)" apply (unfold well_ord_def) -apply (simp add: tot_ord_unit wf_on_unit) +apply (simp add: tot_ord_unit wf_on_any_0) done @@ -676,7 +679,6 @@ val wf_on_0 = thm "wf_on_0"; val well_ord_0 = thm "well_ord_0"; val tot_ord_unit = thm "tot_ord_unit"; -val wf_on_unit = thm "wf_on_unit"; val well_ord_unit = thm "well_ord_unit"; val mono_map_is_fun = thm "mono_map_is_fun"; val mono_map_is_inj = thm "mono_map_is_inj";