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Theorems · Theorem · order theory

le_of_neg_le_neg

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a b : α} [AddRightMono α], -a ≤ -b → b ≤ a

Alias of the forward direction of neg_le_neg_iff.

Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
4 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext
Assumes
AddGroupLEAddLeftMonoAddRightMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AkraBazziRecurrence.GrowsPolynomially.add_isLittleO · cited by 1GrowsPolynomially.add_isL…UniformConvexOn.neg · cited by 1UniformConvexOn.negZsqrtd.Nonneg.add · cited by 1Nonneg.addUniformConcaveOn.neg · cited by 1UniformConcaveOn.negAddGroup · cited by 4410AddGroupAddLeftMono · cited by 687AddLeftMonoAddRightMono · cited by 367AddRightMononeg_le_neg_iff · cited by 57neg_le_neg_iffle_of_neg_le_negCITED BYCITES

Cites4

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

Cited by4

Results whose statement or proof uses this declaration.