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Theorems · Theorem · group theory

mem_fixingSubmonoid_iff

∀ (M : Type u_1) {α : Type u_2} [inst : Monoid M] [inst_1 : MulAction M α] {s : Set α} {m : M},
  m ∈ fixingSubmonoid M s ↔ ∀ y ∈ s, m • y = y
Defined in
Mathlib.GroupTheory.GroupAction.FixingSubgroup
Cited by
0 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
MonoidMulAction
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Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemMonoid · cited by 3887MonoidSubmonoid · cited by 3086SubmonoidMulAction · cited by 1294MulActionfixingSubmonoid · cited by 5fixingSubmonoidmem_fixingSubmonoid_iffCITED BYCITES

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