equal
deleted
inserted
replaced
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" |