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Theorems · Theorem · group theory

Set.pow_mul_subgroupClosure

∀ {G : Type u_2} [inst : Group G] {s : Set G},
  s.Nonempty → ∀ (n : ℕ), s ^ n * ↑(Subgroup.closure s) = ↑(Subgroup.closure s)
Defined in
Mathlib.Algebra.Group.Subgroup.Pointwise
Cited by
1 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Group
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.pow_right_strictMonoOn · cited by 1Finset.pow_right_strictMo…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeGroup · cited by 6238GroupSubgroup · cited by 3593SubgroupSet.Nonempty · cited by 2627Set.NonemptySet.mul · cited by 297Set.mulSubgroup.closure · cited by 196Subgroup.closureSet.monoid · cited by 19Set.monoidSet.pow_mul_subgroupClosureCITED BYCITES

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Cited by1

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