Theorems · Theorem · order theory
antivary_iff_forall_smul_nonpos
∀ {ι : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Ring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α]
[inst_3 : AddCommGroup β] [inst_4 : LinearOrder β] [IsOrderedAddMonoid β] [inst_6 : Module α β]
[IsStrictOrderedModule α β] {f : ι → α} {g : ι → β}, Antivary f g ↔ ∀ (i j : ι), (f j - f i) • (g j - g i) ≤ 0- Defined in
- Mathlib.Algebra.Order.Monovary
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Antivarystatement · cited by 121
- IsStrictOrderedModulestatement and proof · cited by 111
- monovary_iff_forall_smul_nonnegproof · cited by 2
- monovary_toDual_rightproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Antivary.sub_smul_sub_nonposproof · cited by 0