equal
deleted
inserted
replaced
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] |