Theorems · Definition · number theory
MulDissociated
{α : Type u_1} → [CommGroup α] → Set α → PropA set is dissociated iff all its finite subsets have different products.
This is an analog of linear independence in a vector space, but with the "scalars" restricted to
0 and ±1.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 54 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.
Cites7
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Finset.prodproof · cited by 2,356
- CommGroupstatement and proof · cited by 990
- Set.InjOnproof · cited by 543
Cited by11
Results whose statement or proof uses this declaration.
- mulDissociated_invstatement · cited by 2
- not_mulDissociatedstatement · cited by 1
- not_mulDissociated_iff_exists_disjointstatement · cited by 1
- MulEquiv.mulDissociated_preimagestatement · cited by 1
- MulDissociated.of_invstatement · cited by 0
- mulDissociated_emptystatement · cited by 0
- mulDissociated_iff_sum_eq_subsingletonstatement and proof · cited by 0
- mulDissociated_singletonstatement · cited by 0
- MulDissociated.invstatement · cited by 0
- Finset.exists_subset_mulSpan_card_le_of_forall_mulDissociatedstatement and proof · cited by 0
- MulDissociated.subsetstatement and proof · cited by 0