Theorems · Theorem · order theory

MulArchimedeanClass.mem_subgroup_iff

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

Defined in

Mathlib.Algebra.Order.Archimedean.Class

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoid