Theorems · Theorem · group theory
Subgroup.closure_toSubmonoid_of_finite
∀ {G : Type u_1} [inst : Group G] [Finite G] {s : Set G}, (Subgroup.closure s).toSubmonoid = Submonoid.closure sSee Subgroup.closure_toSubmonoid_of_isOfFinOrder for a version with weaker assumptions.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Submonoidstatement · cited by 3,086
- Finitestatement and proof · cited by 3,029
- Subgroup.closurestatement · cited by 196
- Submonoid.closurestatement · cited by 167
- Subgroup.toSubmonoidstatement · cited by 114
- Subgroup.closure_toSubmonoid_of_isOfFinOrderproof · cited by 1
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