Theorems · Theorem · group theory
Subgroup.exists_finsupp_of_mem_closure_range
∀ {M : Type u_1} [inst : CommGroup M] {ι : Type u_2} (f : ι → M),
∀ x ∈ Subgroup.closure (Set.range f), ∃ a, x = a.prod fun x1 x2 => f x1 ^ x2- Defined in
- Mathlib.Algebra.Group.Subgroup.Finsupp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsuppstatement and proof · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- Subgroupstatement · cited by 3,593
- pow_zeroproof · cited by 1,094
- CommGroupstatement and proof · cited by 990
- Finsupp.singleproof · cited by 943
- pow_oneproof · cited by 894
- Finsupp.prodstatement and proof · cited by 231
- zpow_negproof · cited by 198
- Subgroup.closurestatement and proof · cited by 196
- zpow_ofNatproof · cited by 144
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.mem_closure_range_iffproof · cited by 1
- Subgroup.exists_of_mem_closure_rangeproof · cited by 0