Theorems · Theorem · number theory
not_mulDissociated_iff_exists_disjoint
∀ {α : Type u_1} [inst : CommGroup α] {s : Set α},
¬MulDissociated s ↔ ∃ t u, ↑t ⊆ s ∧ ↑u ⊆ s ∧ Disjoint t u ∧ t ≠ u ∧ ∏ a ∈ t, a = ∏ a ∈ u, a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 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.
Cites14
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
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- LE.le.transproof · cited by 3,151
- Finset.prodstatement and proof · cited by 2,356
- Disjointstatement and proof · cited by 2,201
- CommGroupstatement and proof · cited by 990
- Set.sdiff_subsetproof · cited by 156
- Finset.coe_sdiffproof · cited by 23
- MulDissociatedstatement · cited by 11
- disjoint_sdiff_sdiffproof · cited by 6
- sdiff_ne_sdiff_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finset.exists_subset_mulSpan_card_le_of_forall_mulDissociatedproof · cited by 0