src/HOL/Nonstandard_Analysis/NSA.thy
changeset 70723 4e39d87c9737
parent 70232 d19266b7465f
child 73932 fd21b4a93043
equal deleted inserted replaced
70722:ae2528273eeb 70723:4e39d87c9737
  1590 
  1590 
  1591 text \<open>Epsilon is a member of Infinitesimal.\<close>
  1591 text \<open>Epsilon is a member of Infinitesimal.\<close>
  1592 
  1592 
  1593 lemma Infinitesimal_epsilon [simp]: "\<epsilon> \<in> Infinitesimal"
  1593 lemma Infinitesimal_epsilon [simp]: "\<epsilon> \<in> Infinitesimal"
  1594   by (auto intro!: HInfinite_inverse_Infinitesimal HInfinite_omega
  1594   by (auto intro!: HInfinite_inverse_Infinitesimal HInfinite_omega
  1595       simp add: hypreal_epsilon_inverse_omega)
  1595       simp add: epsilon_inverse_omega)
  1596 
  1596 
  1597 lemma HFinite_epsilon [simp]: "\<epsilon> \<in> HFinite"
  1597 lemma HFinite_epsilon [simp]: "\<epsilon> \<in> HFinite"
  1598   by (auto intro: Infinitesimal_subset_HFinite [THEN subsetD])
  1598   by (auto intro: Infinitesimal_subset_HFinite [THEN subsetD])
  1599 
  1599 
  1600 lemma epsilon_approx_zero [simp]: "\<epsilon> \<approx> 0"
  1600 lemma epsilon_approx_zero [simp]: "\<epsilon> \<approx> 0"