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Theorems · Theorem · order theory

antivaryOn_neg

∀ {ι : Type u_1} {α : Type u_2} {β : Type u_3} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α]
  [inst_3 : AddCommGroup β] [inst_4 : PartialOrder β] [IsOrderedAddMonoid β] {s : Set ι} {f : ι → α} {g : ι → β},
  AntivaryOn (-f) (-g) s ↔ AntivaryOn f g s
Defined in
Mathlib.Algebra.Order.Monovary
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupPartialOrderIsOrderedAddMonoidAddCommGroupPartialOrderIsOrderedAddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AntivaryOn.neg · cited by 1AntivaryOn.negAntivaryOn.of_neg · cited by 0AntivaryOn.of_negSet · cited by 53352SetAddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrderIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidAntivaryOn · cited by 138AntivaryOnmonovaryOn_neg_left · cited by 3monovaryOn_neg_leftantivaryOn_neg_right · cited by 3antivaryOn_neg_rightantivaryOn_negCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.