Theorems · Theorem · group theory
AddSubgroup.exists_finsupp_of_mem_closure_range
∀ {M : Type u_1} [inst : AddCommGroup M] {ι : Type u_2} (f : ι → M),
∀ x ∈ AddSubgroup.closure (Set.range f), ∃ a, x = a.sum fun x1 x2 => x2 • f x1- 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
- AddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- Finsuppstatement and proof · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- AddSubgroupstatement · cited by 3,232
- Finsupp.singleproof · cited by 943
- Finsupp.sumstatement and proof · cited by 481
- AddSubgroup.closurestatement and proof · cited by 156
- zero_nsmulproof · cited by 137
- Finsupp.sum_single_indexproof · cited by 130
- Finsupp.mem_support_iffproof · cited by 89
- one_nsmulproof · cited by 63
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_closure_range_iffproof · cited by 1
- AddSubgroup.exists_of_mem_closure_rangeproof · cited by 0