diff -r 29f8b00d7e1f -r 45f837f8889d src/HOL/BCV/Semilat.ML
--- a/src/HOL/BCV/Semilat.ML	Fri Jun 01 11:04:19 2001 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,177 +0,0 @@
-(*  Title:      HOL/BCV/Semilat.ML
-    ID:         $Id$
-    Author:     Tobias Nipkow
-    Copyright   2000 TUM
-*)
-
-Goalw [order_def] "order r ==> x <=_r x";
-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);
-qed "order_antisym";
-
-Goalw [order_def] "[| order r; x <=_r y; y <=_r z |] ==> x <=_r z";
-by (Blast_tac 1);
-qed "order_trans";
-
-Goalw [order_def,lesssub_def] "order r ==> ~ x <_r x";
-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);
-qed "order_less_trans";
-
-Goalw [top_def] "top r T ==> x <=_r T";
-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);
-qed "top_le_conv";
-Addsimps [top_le_conv];
-
-Goalw [semilat_def, split_conv RS eq_reflection]
-"semilat(A,r,f) == order r & closed A f & \
-\                (!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)";
-by (rtac (refl RS eq_reflection) 1);
-qed "semilat_Def";
-
-Goalw [semilat_Def] "semilat(A,r,f) ==> order r";
-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);
-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);
-qed "semilat_ub1";
-
-Goalw [semilat_Def] "[| semilat(A,r,f); x:A; y:A |] ==> y <=_r x +_f y";
-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);
-qed "semilat_lub";
-
-Addsimps [semilat_ub1,semilat_ub2,semilat_lub];
-
-Goalw [semilat_Def]
- "[| x:A; y:A; z:A; semilat(A,r,f) |] ==> \
-\ (x +_f y <=_r z) = (x <=_r z & y <=_r z)";
-by (blast_tac (claset() addIs [semilat_ub1,semilat_ub2,semilat_lub,order_trans]) 1);
-qed "plus_le_conv";
-Addsimps [plus_le_conv];
-
-Goal "[| x:A; y:A; semilat(A,r,f) |] ==> (x <=_r y) = (x +_f y = y)";
-by (rtac iffI 1);
- by (REPEAT(ares_tac [semilatDorderI,order_antisym,semilat_lub,order_refl,semilat_ub2] 1));
-by (etac subst 1);
-by (Asm_simp_tac 1);
-qed "le_iff_plus_unchanged";
-
-Goal "[| x:A; y:A; semilat(A,r,f) |] ==> (x <=_r y) = (y +_f x = y)";
-by (rtac iffI 1);
- by (REPEAT(ares_tac [semilatDorderI,order_antisym,semilat_lub,order_refl,semilat_ub1] 1));
-by (etac subst 1);
-by (Asm_simp_tac 1);
-qed "le_iff_plus_unchanged2";
-
-(*** closed ***)
-
-Goalw [closed_def] "[| closed A f; x:A; y:A |] ==> x +_f y : A";
-by (Blast_tac 1);
-qed "closedD";
-
-Goalw [closed_def] "closed UNIV f";
-by (Simp_tac 1);
-qed "closed_UNIV";
-AddIffs [closed_UNIV];
-
-(*** lub ***)
-
-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)";
-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);
-qed "is_ubI";
-
-Goalw [is_ub_def]
- "is_ub r x y u ==> (x,u) : r & (y,u) : r";
-by (assume_tac 1);
-qed "is_ubD";
-
-
-Goalw [is_lub_def,is_ub_def] "is_lub (r^*) x y y = ((x,y):r^*)";
-by (Blast_tac 1);
-qed "is_lub_bigger1";
-AddIffs [is_lub_bigger1];
-
-Goalw [is_lub_def,is_ub_def] "is_lub (r^*) x y x = ((y,x):r^*)";
-by (Blast_tac 1);
-qed "is_lub_bigger2";
-AddIffs [is_lub_bigger2];
-
-
-Goalw [is_lub_def,is_ub_def]
- "[| single_valued 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 (Blast_tac 1);
- by (blast_tac (claset() addIs [r_into_rtrancl] addEs [converse_rtranclE]
-                        addDs [single_valuedD]) 1);
-by (rtac exI 1);
-by (rtac conjI 1);
- by (blast_tac (claset() addIs [rtrancl_into_rtrancl2]addDs [single_valuedD]) 1);
-by (blast_tac (claset() addIs [rtrancl_into_rtrancl,rtrancl_into_rtrancl2]
-                       addEs [converse_rtranclE] addDs [single_valuedD]) 1);
-qed "extend_lub";
-
-Goal "[| single_valued 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);
-qed_spec_mp "single_valued_has_lubs";
-
-Goalw [some_lub_def,is_lub_def]
- "[| acyclic r; is_lub (r^*) x y u |] ==> some_lub (r^*) x y = u";
-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
- "[| single_valued r; acyclic r; (x,u):r^*; (y,u):r^* |] ==> \
-\ is_lub (r^*) x y (some_lub (r^*) x y)";
-by (fast_tac
-    (claset() addDs [single_valued_has_lubs]
-     addss (simpset() addsimps [some_lub_conv])) 1);
-qed "is_lub_some_lub";