--- a/src/HOL/ex/Group.ML Fri Nov 29 15:07:27 1996 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,127 +0,0 @@
-(* Title: HOL/ex/Group.ML
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 1996 TU Muenchen
-*)
-
-open Group;
-
-Addsimps [zeroL,zeroR,plus_assoc,plus_commute];
-
-goal Group.thy "!!x::'a::add_group. (zero-x)+(x+y) = y";
-br trans 1;
-br (plus_assoc RS sym) 1;
-by(stac left_inv 1);
-br zeroL 1;
-qed "left_inv2";
-
-goal Group.thy "!!x::'a::add_group. (zero-(zero-x)) = x";
-br trans 1;
-by(res_inst_tac [("x","zero-x")] left_inv2 2);
-by(stac left_inv 1);
-br (zeroR RS sym) 1;
-qed "inv_inv";
-
-goal Group.thy "zero-zero = (zero::'a::add_group)";
-br trans 1;
-br (zeroR RS sym) 1;
-br trans 1;
-by(res_inst_tac [("x","zero")] left_inv2 2);
-by(Simp_tac 1);
-qed "inv_zero";
-
-goal Group.thy "!!x::'a::add_group. x+(zero-x) = zero";
-br trans 1;
-by(res_inst_tac [("x","zero-x")] left_inv 2);
-by(stac inv_inv 1);
-br refl 1;
-qed "right_inv";
-
-goal Group.thy "!!x::'a::add_group. x+((zero-x)+y) = y";
-br trans 1;
-by(res_inst_tac [("x","zero-x")] left_inv2 2);
-by(stac inv_inv 1);
-br refl 1;
-qed "right_inv2";
-
-goal Group.thy "!!x::'a::add_group. x-x = zero";
-by(stac minus_inv 1);
-br right_inv 1;
-qed "minus_self_zero";
-Addsimps [minus_self_zero];
-
-goal Group.thy "!!x::'a::add_group. x-zero = x";
-by(stac minus_inv 1);
-by(stac inv_zero 1);
-br zeroR 1;
-qed "minus_zero";
-Addsimps [minus_zero];
-
-val plus_cong = read_instantiate [("f1","op +")] (arg_cong RS cong);
-
-goal Group.thy "!!x::'a::add_group. zero-(x+y) = (zero-y)+(zero-x)";
-br trans 1;
- br zeroR 2;
-br trans 1;
- br plus_cong 2;
- br refl 2;
- by(res_inst_tac [("x","x+y")] right_inv 2);
-br trans 1;
- br plus_assoc 2;
-br trans 1;
- br plus_cong 2;
- by(simp_tac (!simpset addsimps [left_inv,left_inv2,right_inv,right_inv2]) 2);
- br refl 2;
-br (zeroL RS sym) 1;
-qed "inv_plus";
-
-goal Group.thy "x+(y+z)=y+(x+z::'a::add_agroup)";
-br trans 1;
-br plus_commute 1;
-br trans 1;
-br plus_assoc 1;
-by(Simp_tac 1);
-qed "plus_commuteL";
-Addsimps [plus_commuteL];
-
-Addsimps [inv_inv,inv_plus];
-
-(* Phase 1 *)
-
-goal Group.thy "!!x::'a::add_agroup. (x+(zero-y))+z = (x+z)+(zero-y)";
-by(Simp_tac 1);
-val lemma = result();
-bind_thm("plus_minusL",rewrite_rule[minus_inv RS sym RS eq_reflection]lemma);
-
-goal Group.thy "!!x::'a::add_agroup. x+(zero-(y+z)) = (x+(zero-y))+(zero-z)";
-by(Simp_tac 1);
-val lemma = result();
-bind_thm("minus_plusR",rewrite_rule[minus_inv RS sym RS eq_reflection]lemma);
-
-goal Group.thy "!!x::'a::add_agroup. x+(zero-(y+(zero-z))) = (x+z)+(zero-y)";
-by(Simp_tac 1);
-val lemma = result();
-bind_thm("minus_minusR",rewrite_rule[minus_inv RS sym RS eq_reflection]lemma);
-
-goal Group.thy "!!x::'a::add_agroup. x+(y+(zero-z)) = (x+y)+(zero-z)";
-by(Simp_tac 1);
-val lemma = result();
-bind_thm("plus_minusR",rewrite_rule[minus_inv RS sym RS eq_reflection]lemma);
-
-(* Phase 2 *)
-
-goal Group.thy "!!x::'a::add_agroup. (x+y)+(zero-z) = x+(y+(zero-z))";
-by(Simp_tac 1);
-val lemma = result();
-bind_thm("minus_plusL2",rewrite_rule[minus_inv RS sym RS eq_reflection]lemma);
-
-goal Group.thy "!!x::'a::add_agroup. (x+y)+(zero-x) = y";
-br (plus_assoc RS trans) 1;
-br trans 1;
- br plus_cong 1;
- br refl 1;
- br right_inv2 2;
-br plus_commute 1;
-val lemma = result();
-bind_thm("minus_plusL3",rewrite_rule[minus_inv RS sym RS eq_reflection]lemma);
-