Theorems · Theorem · group theory
Subgroup.exists_of_mem_closure_range
∀ {M : Type u_1} [inst : CommGroup M] {ι : Type u_2} (f : ι → M) (x : M) [inst_1 : Fintype ι],
x ∈ Subgroup.closure (Set.range f) → ∃ a, x = ∏ i, f i ^ a i- Defined in
- Mathlib.Algebra.Group.Subgroup.Finsupp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Finsuppproof · cited by 5,255
- Set.rangestatement and proof · 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
- Finsupp.prodproof · cited by 231
- Subgroup.closurestatement and proof · cited by 196
- Subgroup.exists_finsupp_of_mem_closure_rangeproof · cited by 2
- Finsupp.prod_zpowproof · cited by 2
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