src/ZF/OrderArith.ML
changeset 782 200a16083201
parent 770 216ec1299bf0
child 815 de2d8a63256d
equal deleted inserted replaced
781:9ab8873bf9b3 782:200a16083201
    56 
    56 
    57 goalw OrderArith.thy [radd_def] "radd(A,r,B,s) <= (A+B) * (A+B)";
    57 goalw OrderArith.thy [radd_def] "radd(A,r,B,s) <= (A+B) * (A+B)";
    58 by (rtac Collect_subset 1);
    58 by (rtac Collect_subset 1);
    59 qed "radd_type";
    59 qed "radd_type";
    60 
    60 
    61 val field_radd = standard (radd_type RS field_rel_subset);
    61 bind_thm ("field_radd", (radd_type RS field_rel_subset));
    62 
    62 
    63 (** Linearity **)
    63 (** Linearity **)
    64 
    64 
    65 val radd_ss = sum_ss addsimps [radd_Inl_iff, radd_Inr_iff, 
    65 val radd_ss = sum_ss addsimps [radd_Inl_iff, radd_Inr_iff, 
    66 			       radd_Inl_Inr_iff, radd_Inr_Inl_iff];
    66 			       radd_Inl_Inr_iff, radd_Inr_Inl_iff];
   135 
   135 
   136 goalw OrderArith.thy [rmult_def] "rmult(A,r,B,s) <= (A*B) * (A*B)";
   136 goalw OrderArith.thy [rmult_def] "rmult(A,r,B,s) <= (A*B) * (A*B)";
   137 by (rtac Collect_subset 1);
   137 by (rtac Collect_subset 1);
   138 qed "rmult_type";
   138 qed "rmult_type";
   139 
   139 
   140 val field_rmult = standard (rmult_type RS field_rel_subset);
   140 bind_thm ("field_rmult", (rmult_type RS field_rel_subset));
   141 
   141 
   142 (** Linearity **)
   142 (** Linearity **)
   143 
   143 
   144 val [lina,linb] = goal OrderArith.thy
   144 val [lina,linb] = goal OrderArith.thy
   145     "[| linear(A,r);  linear(B,s) |] ==> linear(A*B,rmult(A,r,B,s))";
   145     "[| linear(A,r);  linear(B,s) |] ==> linear(A*B,rmult(A,r,B,s))";
   200 
   200 
   201 goalw OrderArith.thy [rvimage_def] "rvimage(A,f,r) <= A*A";
   201 goalw OrderArith.thy [rvimage_def] "rvimage(A,f,r) <= A*A";
   202 by (rtac Collect_subset 1);
   202 by (rtac Collect_subset 1);
   203 qed "rvimage_type";
   203 qed "rvimage_type";
   204 
   204 
   205 val field_rvimage = standard (rvimage_type RS field_rel_subset);
   205 bind_thm ("field_rvimage", (rvimage_type RS field_rel_subset));
   206 
   206 
   207 
   207 
   208 (** Linearity **)
   208 (** Linearity **)
   209 
   209 
   210 val [finj,lin] = goalw OrderArith.thy [inj_def]
   210 val [finj,lin] = goalw OrderArith.thy [inj_def]