--- a/src/ZF/WF.ML Thu Jun 23 16:44:57 1994 +0200
+++ b/src/ZF/WF.ML Thu Jun 23 17:38:12 1994 +0200
@@ -62,7 +62,7 @@
"[| !!y B. [| ALL x:A. (ALL y:A. <y,x>:r --> y:B) --> x:B; y:A \
\ |] ==> y:B |] \
\ ==> wf[A](r)";
-br wf_onI 1;
+by (rtac wf_onI 1);
by (res_inst_tac [ ("c", "u") ] (prem RS DiffE) 1);
by (contr_tac 3);
by (fast_tac ZF_cs 2);
@@ -131,7 +131,7 @@
\ !!y B. [| ALL x:A. (ALL y:A. <y,x>:r --> y:B) --> x:B; y:A \
\ |] ==> y:B |] \
\ ==> wf(r)";
-br ([wf_onI2, subs] MRS (wf_on_subset_A RS wf_on_field_imp_wf)) 1;
+by (rtac ([wf_onI2, subs] MRS (wf_on_subset_A RS wf_on_field_imp_wf)) 1);
by (REPEAT (ares_tac [indhyp] 1));
val wfI2 = result();
@@ -148,7 +148,7 @@
by (wf_ind_tac "a" [] 2);
by (fast_tac ZF_cs 2);
by (fast_tac FOL_cs 1);
-val wf_anti_sym = result();
+val wf_asym = result();
goal WF.thy "!!r. [| wf[A](r); a: A |] ==> <a,a> ~: r";
by (wf_on_ind_tac "a" [] 1);
@@ -160,7 +160,7 @@
by (wf_on_ind_tac "a" [] 2);
by (fast_tac ZF_cs 2);
by (fast_tac ZF_cs 1);
-val wf_on_anti_sym = result();
+val wf_on_asym = result();
(*Needed to prove well_ordI. Could also reason that wf[A](r) means
wf(r Int A*A); thus wf( (r Int A*A)^+ ) and use wf_not_refl *)
@@ -180,7 +180,7 @@
(*transitive closure of a WF relation is WF provided A is downwards closed*)
val [wfr,subs] = goal WF.thy
"[| wf[A](r); r-``A <= A |] ==> wf[A](r^+)";
-br wf_onI2 1;
+by (rtac wf_onI2 1);
by (bchain_tac 1);
by (eres_inst_tac [("a","y")] (wfr RS wf_on_induct) 1);
by (rtac (impI RS ballI) 1);
@@ -194,8 +194,8 @@
goal WF.thy "!!r. wf(r) ==> wf(r^+)";
by (asm_full_simp_tac (ZF_ss addsimps [wf_iff_wf_on_field]) 1);
-br (trancl_type RS field_rel_subset RSN (2, wf_on_subset_A)) 1;
-be wf_on_trancl 1;
+by (rtac (trancl_type RS field_rel_subset RSN (2, wf_on_subset_A)) 1);
+by (etac wf_on_trancl 1);
by (fast_tac ZF_cs 1);
val wf_trancl = result();
@@ -342,7 +342,7 @@
goalw WF.thy [wf_on_def, wfrec_on_def]
"!!A r. [| wf[A](r); a: A |] ==> \
\ wfrec[A](r,a,H) = H(a, lam x: (r-``{a}) Int A. wfrec[A](r,x,H))";
-be (wfrec RS trans) 1;
+by (etac (wfrec RS trans) 1);
by (asm_simp_tac (ZF_ss addsimps [vimage_Int_square, cons_subset_iff]) 1);
val wfrec_on = result();