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Theorems · Theorem · group theory

fixedPoints_submonoid_sup

∀ (M : Type u_1) (α : Type u_2) [inst : Monoid M] [inst_1 : MulAction M α] {P Q : Submonoid M},
  MulAction.fixedPoints (↥(P ⊔ Q)) α = MulAction.fixedPoints (↥P) α ∩ MulAction.fixedPoints (↥Q) α

Fixed points of sup of submonoids is intersection

Defined in
Mathlib.GroupTheory.GroupAction.FixingSubgroup
Cited by
0 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidMulAction
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Set · cited by 53352SetMonoid · cited by 3887MonoidSubmonoid · cited by 3086SubmonoidMulAction · cited by 1294MulActionMulAction.fixedPoints · cited by 41MulAction.fixedPointsGaloisConnection.u_inf · cited by 37GaloisConnection.u_inffixingSubmonoid_fixedPoints_gc · cited by 6fixingSubmonoid_fixedPoin…fixedPoints_submonoid_supCITED BYCITES

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