Theorems · Theorem · order theory
antivaryOn_neg_right
∀ {ι : Type u_1} {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : AddCommGroup β]
[inst_2 : PartialOrder β] [IsOrderedAddMonoid β] {s : Set ι} {f : ι → α} {g : ι → β},
AntivaryOn f (-g) s ↔ MonovaryOn f g s- Defined in
- Mathlib.Algebra.Order.Monovary
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- MonovaryOnstatement · cited by 139
- AntivaryOnstatement · cited by 138
- neg_lt_neg_iffproof · cited by 39
- forall₂_commproof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- antivaryOn_negproof · cited by 2
- MonovaryOn.neg_rightproof · cited by 2
- AntivaryOn.of_neg_rightproof · cited by 0