Theorems · Theorem · order theory

FiniteMulArchimedeanClass.mem_subgroup_iff

∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a : M}
  {s : UpperSet (FiniteMulArchimedeanClass M)},
  a ∈ FiniteMulArchimedeanClass.subgroup s ↔ ∀ (h : a ≠ 1), FiniteMulArchimedeanClass.mk a h ∈ s

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoid