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Theorems · Theorem · order theory

Right.neg_pos_iff

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

Uses right co(ntra)variant.

Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
2 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Assumes
AddGroupLTAddRightStrictMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Module.Ray.units_smul_of_neg · cited by 0Ray.units_smul_of_negRight.self_lt_neg · cited by 0Right.self_lt_negAddGroup · cited by 4410AddGroupzero_add · cited by 2366zero_addneg_add_cancel · cited by 256neg_add_cancelAddRightStrictMono · cited by 160AddRightStrictMonoadd_lt_add_iff_right · cited by 42add_lt_add_iff_rightRight.neg_pos_iffCITED BYCITES

Cites5

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.