src/HOL/NSA/NSCA.thy
changeset 37887 2ae085b07f2f
parent 37765 26bdfb7b680b
child 47108 2a1953f0d20d
equal deleted inserted replaced
37886:2f9d3fc1a8ac 37887:2ae085b07f2f
   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"