src/HOL/Hyperreal/NSA.thy
changeset 20217 25b068a99d2b
parent 19765 dfe940911617
child 20254 58b71535ed00
equal deleted inserted replaced
20216:f30b73385060 20217:25b068a99d2b
  1347 lemma Infinitesimal_add_hypreal_of_real_less:
  1347 lemma Infinitesimal_add_hypreal_of_real_less:
  1348      "[| x < y;  u \<in> Infinitesimal |]
  1348      "[| x < y;  u \<in> Infinitesimal |]
  1349       ==> hypreal_of_real x + u < hypreal_of_real y"
  1349       ==> hypreal_of_real x + u < hypreal_of_real y"
  1350 apply (simp add: Infinitesimal_def)
  1350 apply (simp add: Infinitesimal_def)
  1351 apply (drule_tac x = "hypreal_of_real y + -hypreal_of_real x" in bspec, simp)
  1351 apply (drule_tac x = "hypreal_of_real y + -hypreal_of_real x" in bspec, simp)
  1352 apply (simp add: abs_less_iff)
  1352 (* FIXME: arith simproc bug with   apply (simp add: abs_less_iff) *)
       
  1353 apply simp
  1353 done
  1354 done
  1354 
  1355 
  1355 lemma Infinitesimal_add_hrabs_hypreal_of_real_less:
  1356 lemma Infinitesimal_add_hrabs_hypreal_of_real_less:
  1356      "[| x \<in> Infinitesimal; abs(hypreal_of_real r) < hypreal_of_real y |]
  1357      "[| x \<in> Infinitesimal; abs(hypreal_of_real r) < hypreal_of_real y |]
  1357       ==> abs (hypreal_of_real r + x) < hypreal_of_real y"
  1358       ==> abs (hypreal_of_real r + x) < hypreal_of_real y"