author wenzelm Thu, 01 Jul 1999 17:42:27 +0200 changeset 6873 b123f5522ea1 parent 6872 b250da153b1e child 6874 747f656e04ec
tuned;
 src/HOL/Calculation.thy file | annotate | diff | comparison | revisions
```--- a/src/HOL/Calculation.thy	Thu Jul 01 17:41:16 1999 +0200
+++ b/src/HOL/Calculation.thy	Thu Jul 01 17:42:27 1999 +0200
@@ -2,33 +2,34 @@
ID:         \$Id\$
Author:     Markus Wenzel, TU Muenchen

-Setup transitivity rules for calculational proofs.
+Setup transitivity rules for calculational proofs.  Note that in the
+list below later rules have priority.
*)

theory Calculation = Int:;

-theorems [trans] = Ord.order_antisym;                   (*  <= <= =  *)
-theorems [trans] = Ord.order_trans;                     (*  <= <= <= *)
+theorems [trans] = HOL.ssubst;                          (*  =  x  x  *)
+theorems [trans] = HOL.subst[COMP swap_prems_rl];       (*  x  =  x  *)
+
+theorems [trans] = Divides.dvd_trans;                   (* dvd dvd dvd *)
+
theorems [trans] = Ord.order_less_trans;                (*  <  <  <  *)
theorems [trans] = Ord.order_le_less_trans;             (*  <= <  <  *)
theorems [trans] = Ord.order_less_le_trans;             (*  <  <= <  *)
+theorems [trans] = Ord.order_trans;                     (*  <= <= <= *)
+theorems [trans] = Ord.order_antisym;                   (*  <= <= =  *)

theorem [trans]: "[| x <= y; y = z |] ==> x <= z";	(*  <= =  <= *)
-  by (rule HOL.subst[with y z]);
+  by (rule HOL.subst);

theorem [trans]: "[| x = y; y <= z |] ==> x <= z";	(*  =  <= <= *)
-  by (rule HOL.ssubst[with x y]);
+  by (rule HOL.ssubst);

theorem [trans]: "[| x < y; y = z |] ==> x < z";	(*  <  =  <  *)
-  by (rule HOL.subst[with y z]);
+  by (rule HOL.subst);

theorem [trans]: "[| x = y; y < z |] ==> x < z";	(*  =  <  <  *)
-  by (rule HOL.ssubst[with x y]);
-
-theorems [trans] = HOL.subst[COMP swap_prems_rl];       (*  x  =  x  *)
-theorems [trans] = HOL.ssubst;                          (*  =  x  x  *)
-
-theorems [trans] = Divides.dvd_trans;                   (* dvd dvd dvd *)
+  by (rule HOL.ssubst);

end;```