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Theorems · Theorem · group theory

Submonoid.closure_eq_of_le

∀ {M : Type u_1} [inst : MulOneClass M] {s : Set M} {S : Submonoid M},
  s ⊆ ↑S → S ≤ Submonoid.closure s → Submonoid.closure s = S
Defined in
Mathlib.Algebra.Group.Submonoid.Basic
Cited by
2 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulOneClass
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Around this declaration

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

MonoidWithZeroHom.valueMonoid_eq_valueGroup · cited by 1MonoidWithZeroHom.valueMo…Submonoid.closure_singleton_eq · cited by 1Submonoid.closure_singlet…Set · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeSubmonoid · cited by 3086Submonoidle_antisymm · cited by 2068le_antisymmMulOneClass · cited by 1018MulOneClassSubmonoid.closure · cited by 167Submonoid.closureSubmonoid.closure_le · cited by 27Submonoid.closure_leSubmonoid.closure_eq_of_leCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.