--- a/src/HOL/AxClasses/Tutorial/Group.ML Mon May 22 13:20:47 2000 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,116 +0,0 @@
-(* Title: HOL/AxClasses/Tutorial/Group.ML
- ID: $Id$
- Author: Markus Wenzel, TU Muenchen
-
-Some basic theorems of group theory.
-*)
-
-fun sub r = standard (r RS subst);
-fun ssub r = standard (r RS ssubst);
-
-
-Goal "x <*> inverse x = (1::'a::group)";
-by (rtac (sub left_unit) 1);
-back();
-by (rtac (sub assoc) 1);
-by (rtac (sub left_inverse) 1);
-back();
-back();
-by (rtac (ssub assoc) 1);
-back();
-by (rtac (ssub left_inverse) 1);
-by (rtac (ssub assoc) 1);
-by (rtac (ssub left_unit) 1);
-by (rtac (ssub left_inverse) 1);
-by (rtac refl 1);
-qed "right_inverse";
-
-
-Goal "x <*> 1 = (x::'a::group)";
-by (rtac (sub left_inverse) 1);
-by (rtac (sub assoc) 1);
-by (rtac (ssub right_inverse) 1);
-by (rtac (ssub left_unit) 1);
-by (rtac refl 1);
-qed "right_unit";
-
-
-Goal "e <*> x = x --> e = (1::'a::group)";
-by (rtac impI 1);
-by (rtac (sub right_unit) 1);
-back();
-by (res_inst_tac [("x", "x")] (sub right_inverse) 1);
-by (rtac (sub assoc) 1);
-by (rtac arg_cong 1);
-back();
-by (assume_tac 1);
-qed "strong_one_unit";
-
-
-Goal "EX! e. ALL x. e <*> x = (x::'a::group)";
-by (rtac ex1I 1);
-by (rtac allI 1);
-by (rtac left_unit 1);
-by (rtac mp 1);
-by (rtac strong_one_unit 1);
-by (etac allE 1);
-by (assume_tac 1);
-qed "ex1_unit";
-
-
-Goal "ALL x. EX! e. e <*> x = (x::'a::group)";
-by (rtac allI 1);
-by (rtac ex1I 1);
-by (rtac left_unit 1);
-by (rtac (strong_one_unit RS mp) 1);
-by (assume_tac 1);
-qed "ex1_unit'";
-
-
-Goal "y <*> x = 1 --> y = inverse (x::'a::group)";
-by (rtac impI 1);
-by (rtac (sub right_unit) 1);
-back();
-back();
-by (rtac (sub right_unit) 1);
-by (res_inst_tac [("x", "x")] (sub right_inverse) 1);
-by (rtac (sub assoc) 1);
-by (rtac (sub assoc) 1);
-by (rtac arg_cong 1);
-back();
-by (rtac (ssub left_inverse) 1);
-by (assume_tac 1);
-qed "one_inverse";
-
-
-Goal "ALL x. EX! y. y <*> x = (1::'a::group)";
-by (rtac allI 1);
-by (rtac ex1I 1);
-by (rtac left_inverse 1);
-by (rtac mp 1);
-by (rtac one_inverse 1);
-by (assume_tac 1);
-qed "ex1_inverse";
-
-
-Goal "inverse (x <*> y) = inverse y <*> inverse (x::'a::group)";
-by (rtac sym 1);
-by (rtac mp 1);
-by (rtac one_inverse 1);
-by (rtac (ssub assoc) 1);
-by (rtac (sub assoc) 1);
-back();
-by (rtac (ssub left_inverse) 1);
-by (rtac (ssub left_unit) 1);
-by (rtac (ssub left_inverse) 1);
-by (rtac refl 1);
-qed "inverse_product";
-
-
-Goal "inverse (inverse x) = (x::'a::group)";
-by (rtac sym 1);
-by (rtac (one_inverse RS mp) 1);
-by (rtac (ssub right_inverse) 1);
-by (rtac refl 1);
-qed "inverse_inv";
-