Mathlib Map

Theorems · Theorem · order theory

nonneg_of_neg_nonpos

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] {a : α}, -a ≤ 0 → 0 ≤ a

Alias of the forward direction of Left.neg_nonpos_iff. Uses left co(ntra)variant.

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

Around this declaration

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

selfZPow_mul_neg · cited by 3selfZPow_mul_negAddGroup · cited by 4410AddGroupAddLeftMono · cited by 687AddLeftMonoLeft.neg_nonpos_iff · cited by 14Left.neg_nonpos_iffnonneg_of_neg_nonposCITED BYCITES

Cites3

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

Cited by1

Results whose statement or proof uses this declaration.