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Theorems · Theorem · order theory

StrictAnti.add

∀ {α : Type u_1} {β : Type u_2} [inst : Add α] [inst_1 : Preorder α] [inst_2 : Preorder β] {f g : β → α}
  [AddLeftStrictMono α] [AddRightStrictMono α], StrictAnti f → StrictAnti g → StrictAnti fun x => f x + g x

The sum of two strictly antitone functions is strictly antitone.

Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
1 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
AddPreorderPreorderAddLeftStrictMonoAddRightStrictMono
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Around this declaration

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

AkraBazziRecurrence.strictAnti_sumCoeffsExp · cited by 1AkraBazziRecurrence.stric…Preorder · cited by 7952PreorderStrictAnti · cited by 204StrictAntiAddLeftStrictMono · cited by 203AddLeftStrictMonoAddRightStrictMono · cited by 160AddRightStrictMonoadd_lt_add_of_lt_of_lt · cited by 13add_lt_add_of_lt_of_ltStrictAnti.addCITED BYCITES

Cites5

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Cited by1

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