Theorems · Theorem · combinatorics
Finset.ruzsa_triangle_inequality_negAdd_negAdd_negAdd
∀ {G : Type u_1} [inst : DecidableEq G] [inst_1 : AddGroup G] (A B C : Finset G),
B.card * (-A + C).card ≤ (-B + A).card * (-B + C).cardRuzsa's triangle inequality. Negadd-negadd-negadd version.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqAddGroup
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.
- Finsetstatement and proof · cited by 13,712
- AddGroupstatement and proof · cited by 4,410
- Finset.cardstatement and proof · cited by 2,327
- mul_commproof · cited by 2,262
- sub_eq_add_negproof · cited by 1,023
- Finset.mapproof · cited by 747
- Equiv.toEmbeddingproof · cited by 254
- Finset.addstatement · cited by 133
- Finset.card_mapproof · cited by 114
- Finset.negstatement · cited by 63
- AddOpposite.opEquivproof · cited by 20
- Finset.ruzsa_triangle_inequality_sub_sub_subproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Finset.ruzsa_triangle_inequality_negAdd_add_addproof · cited by 1