Dear all,

how about adding the following lemmas to the order class?

lemma (in order) rtranclp_less_eq [simp]:
  "(op ≤)⇧*⇧* = op ≤"
  by (intro ext) (auto elim: rtranclp_induct)

lemma (in order) tranclp_less [simp]:
  "(op <)⇧+⇧+ = op <"
  by (intro ext) (auto elim: tranclp_induct)

lemma (in order) rtranclp_greater_eq [simp]:
  "(op ≥)⇧*⇧* = op ≥"
  by (intro ext) (auto elim: rtranclp_induct)

lemma (in order) tranclp_greater [simp]:
  "(op >)⇧+⇧+ = op >"
  by (intro ext) (auto elim: tranclp_induct)

cheers

chris
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