author lcp Wed, 14 Dec 1994 16:54:13 +0100 changeset 786 2a871417e7fc parent 785 c2ef808dc938 child 787 1affbb1c5f1f
 src/ZF/Order.thy file | annotate | diff | comparison | revisions
```--- a/src/ZF/Order.thy	Wed Dec 14 16:51:16 1994 +0100
+++ b/src/ZF/Order.thy	Wed Dec 14 16:54:13 1994 +0100
@@ -11,8 +11,10 @@
part_ord        :: "[i,i]=>o"		(*Strict partial ordering*)
linear, tot_ord :: "[i,i]=>o"		(*Strict total ordering*)
well_ord        :: "[i,i]=>o"		(*Well-ordering*)
+  mono_map        :: "[i,i,i,i]=>i"	(*Order-preserving maps*)
ord_iso         :: "[i,i,i,i]=>i"	(*Order isomorphisms*)
pred            :: "[i,i,i]=>i"	(*Set of predecessors*)
+  ord_iso_map     :: "[i,i,i,i]=>i"	(*Construction for linearity theorem*)

defs
part_ord_def "part_ord(A,r) == irrefl(A,r) & trans[A](r)"
@@ -23,9 +25,17 @@

well_ord_def "well_ord(A,r) == tot_ord(A,r) & wf[A](r)"

+  mono_map_def "mono_map(A,r,B,s) == \
+\                   {f: A->B. ALL x:A. ALL y:A. <x,y>:r --> <f`x,f`y>:s}"
+
ord_iso_def  "ord_iso(A,r,B,s) == \
\                   {f: bij(A,B). ALL x:A. ALL y:A. <x,y>:r <-> <f`x,f`y>:s}"

pred_def     "pred(A,x,r) == {y:A. <y,x>:r}"

+  ord_iso_map_def
+     "ord_iso_map(A,r,B,s) == \
+\       UN x:A. UN y:B. UN f: ord_iso(pred(A,x,r), r, pred(B,y,s), s).   \
+\            {<x,y>}"
+
end```