Theorems · Theorem · group theory
Subgroup.mem_closure_iff_of_fintype
∀ {M : Type u_1} [inst : CommGroup M] {x : M} {s : Set M} [inst_1 : Fintype ↑s],
x ∈ Subgroup.closure s ↔ ∃ a, x = ∏ i, ↑i ^ a i- Defined in
- Mathlib.Algebra.Group.Subgroup.Finsupp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
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
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Subgroupstatement · cited by 3,593
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- CommGroupstatement and proof · cited by 990
- Subgroup.closurestatement and proof · cited by 196
- Subtype.range_coeproof · cited by 98
- Subgroup.mem_closure_range_iff_of_fintypeproof · cited by 1
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