equal
deleted
inserted
replaced
176 |
176 |
177 lemma Infinitesimal_hcmod_add_diff: |
177 lemma Infinitesimal_hcmod_add_diff: |
178 "u @= 0 ==> hcmod(x + u) - hcmod x \<in> Infinitesimal" |
178 "u @= 0 ==> hcmod(x + u) - hcmod x \<in> Infinitesimal" |
179 apply (drule approx_approx_zero_iff [THEN iffD1]) |
179 apply (drule approx_approx_zero_iff [THEN iffD1]) |
180 apply (rule_tac e = "hcmod u" and e' = "- hcmod u" in Infinitesimal_interval2) |
180 apply (rule_tac e = "hcmod u" and e' = "- hcmod u" in Infinitesimal_interval2) |
181 apply (auto simp add: mem_infmal_iff [symmetric] diff_def) |
181 apply (auto simp add: mem_infmal_iff [symmetric] diff_minus) |
182 apply (rule_tac c1 = "hcmod x" in add_le_cancel_left [THEN iffD1]) |
182 apply (rule_tac c1 = "hcmod x" in add_le_cancel_left [THEN iffD1]) |
183 apply (auto simp add: diff_minus [symmetric]) |
183 apply (auto simp add: diff_minus [symmetric]) |
184 done |
184 done |
185 |
185 |
186 lemma approx_hcmod_add_hcmod: "u @= 0 ==> hcmod(x + u) @= hcmod x" |
186 lemma approx_hcmod_add_hcmod: "u @= 0 ==> hcmod(x + u) @= hcmod x" |