src/HOL/Integ/Group.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Integ/Group.ML	Fri Nov 29 15:11:37 1996 +0100
@@ -0,0 +1,127 @@
+(*  Title:      HOL/Integ/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);
+