src/HOL/BCV/Semilat.ML

--- a/src/HOL/BCV/Semilat.ML	Mon Oct 09 10:18:21 2000 +0200
+++ b/src/HOL/BCV/Semilat.ML	Mon Oct 09 12:23:45 2000 +0200
@@ -5,37 +5,37 @@
 *)
 
 Goalw [order_def] "order r ==> x <=_r x";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "order_refl";
 Addsimps [order_refl];
 AddIs [order_refl];
 
 Goalw [order_def] "[| order r; x <=_r y; y <=_r x |] ==> x = y";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "order_antisym";
 
 Goalw [order_def] "[| order r; x <=_r y; y <=_r z |] ==> x <=_r z";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "order_trans";
 
 Goalw [order_def,lesssub_def] "order r ==> ~ x <_r x";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "order_less_irrefl";
 AddIs [order_less_irrefl];
 Addsimps [order_less_irrefl];
 
 Goalw [order_def,lesssub_def] "[| order r; x <_r y; y <_r z |] ==> x <_r z";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "order_less_trans";
 
 Goalw [top_def] "top r T ==> x <=_r T";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "topD";
 Addsimps [topD];
 AddIs [topD];
 
 Goal "[| order r; top r T |] ==> (T <=_r x) = (x = T)";
-by(blast_tac (claset() addIs [order_antisym]) 1);
+by (blast_tac (claset() addIs [order_antisym]) 1);
 qed "top_le_conv";
 Addsimps [top_le_conv];
 
@@ -44,32 +44,32 @@
 \                (!x:A. !y:A. x <=_r x +_f y)  & \
 \                (!x:A. !y:A. y <=_r x +_f y)  & \
 \                (!x:A. !y:A. !z:A. x <=_r z & y <=_r z --> x +_f y <=_r z)";
-br (refl RS eq_reflection) 1;
+by (rtac (refl RS eq_reflection) 1);
 qed "semilat_Def";
 
 Goalw [semilat_Def] "semilat(A,r,f) ==> order r";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "semilatDorderI";
 Addsimps [semilatDorderI];
 AddIs [semilatDorderI];
 
 Goalw [semilat_Def] "semilat(A,r,f) ==> closed A f";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "semilatDclosedI";
 Addsimps [semilatDclosedI];
 AddIs [semilatDclosedI];
 
 Goalw [semilat_Def] "[| semilat(A,r,f); x:A; y:A |] ==> x <=_r x +_f y";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "semilat_ub1";
 
 Goalw [semilat_Def] "[| semilat(A,r,f); x:A; y:A |] ==> y <=_r x +_f y";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "semilat_ub2";
 
 Goalw [semilat_Def]
  "[| x <=_r z; y <=_r z; semilat(A,r,f); x:A; y:A; z:A |] ==> x +_f y <=_r z";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "semilat_lub";
 
 Addsimps [semilat_ub1,semilat_ub2,semilat_lub];
@@ -98,11 +98,11 @@
 (*** closed ***)
 
 Goalw [closed_def] "[| closed A f; x:A; y:A |] ==> x +_f y : A";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "closedD";
 
 Goalw [closed_def] "closed UNIV f";
-by(Simp_tac 1);
+by (Simp_tac 1);
 qed "closed_UNIV";
 AddIffs [closed_UNIV];
 
@@ -110,17 +110,17 @@
 
 Goalw [is_lub_def]
  "is_lub r x y u ==> is_ub r x y u & (!z. is_ub r x y z --> (u,z):r)";
-ba 1;
+by (assume_tac 1);
 qed "is_lubD";
 
 Goalw [is_ub_def]
  "[| (x,u) : r; (y,u) : r |] ==> is_ub r x y u";
-by(Asm_simp_tac 1);
+by (Asm_simp_tac 1);
 qed "is_ubI";
 
 Goalw [is_ub_def]
  "is_ub r x y u ==> (x,u) : r & (y,u) : r";
-ba 1;
+by (assume_tac 1);
 qed "is_ubD";
 
 
@@ -138,40 +138,40 @@
 Goalw [is_lub_def,is_ub_def]
  "[| univalent r; is_lub (r^*) x y u; (x',x) : r |] ==> \
 \    EX v. is_lub (r^*) x' y v";
-by(case_tac "(y,x) : r^*" 1);
- by(case_tac "(y,x') : r^*" 1);
+by (case_tac "(y,x) : r^*" 1);
+ by (case_tac "(y,x') : r^*" 1);
   by (Blast_tac 1);
- by(blast_tac (claset() addIs [r_into_rtrancl] addEs [converse_rtranclE]
+ by (blast_tac (claset() addIs [r_into_rtrancl] addEs [converse_rtranclE]
                         addDs [univalentD]) 1);
-br exI 1;
-br conjI 1;
- by(blast_tac (claset() addIs [rtrancl_into_rtrancl2]addDs [univalentD]) 1);
-by(blast_tac (claset() addIs [rtrancl_into_rtrancl,rtrancl_into_rtrancl2]
+by (rtac exI 1);
+by (rtac conjI 1);
+ by (blast_tac (claset() addIs [rtrancl_into_rtrancl2]addDs [univalentD]) 1);
+by (blast_tac (claset() addIs [rtrancl_into_rtrancl,rtrancl_into_rtrancl2]
                        addEs [converse_rtranclE] addDs [univalentD]) 1);
 qed "extend_lub";
 
 Goal "[| univalent r; (x,u) : r^* |] ==> (!y. (y,u) : r^* --> \
 \     (EX z. is_lub (r^*) x y z))";
-by(etac converse_rtrancl_induct 1);
- by(Clarify_tac 1);
- by(etac converse_rtrancl_induct 1);
-  by(Blast_tac 1);
- by(blast_tac (claset() addIs [rtrancl_into_rtrancl2]) 1);
-by(blast_tac (claset() addIs [extend_lub]) 1);
+by (etac converse_rtrancl_induct 1);
+ by (Clarify_tac 1);
+ by (etac converse_rtrancl_induct 1);
+  by (Blast_tac 1);
+ by (blast_tac (claset() addIs [rtrancl_into_rtrancl2]) 1);
+by (blast_tac (claset() addIs [extend_lub]) 1);
 qed_spec_mp "univalent_has_lubs";
 
 Goalw [some_lub_def,is_lub_def]
  "[| acyclic r; is_lub (r^*) x y u |] ==> some_lub (r^*) x y = u";
-br someI2 1;
- ba 1;
-by(blast_tac (claset() addIs [antisymD]
+by (rtac someI2 1);
+ by (assume_tac 1);
+by (blast_tac (claset() addIs [antisymD]
                        addSDs [acyclic_impl_antisym_rtrancl]) 1);
 qed "some_lub_conv";
 
 Goal
  "[| univalent r; acyclic r; (x,u):r^*; (y,u):r^* |] ==> \
 \ is_lub (r^*) x y (some_lub (r^*) x y)";
-by(fast_tac
+by (fast_tac
     (claset() addDs [univalent_has_lubs]
      addss (simpset() addsimps [some_lub_conv])) 1);
 qed "is_lub_some_lub";