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Theorems · Theorem · order theory

neg_neg_iff_pos

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a : α}, -a < 0 ↔ 0 < a

Alias of Left.neg_neg_iff. Uses left co(ntra)variant.

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

Around this declaration

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

neg_neg_of_pos · cited by 227neg_neg_of_posexp_neg_integrableOn_Ioi · cited by 2exp_neg_integrableOn_IoiAddGroup · cited by 4410AddGroupAddLeftStrictMono · cited by 203AddLeftStrictMonoLeft.neg_neg_iff · cited by 16Left.neg_neg_iffneg_neg_iff_posCITED BYCITES

Cites3

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.