Theorems · Theorem · order theory

Left.neg_lt_self

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

Defined in: Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 15 from the axioms · uses propext
Assumes: AddGroup Preorder AddLeftStrictMono

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Cites5

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

Preorderstatement and proof · cited by 7,952
AddGroupstatement and proof · cited by 4,410
LT.lt.transproof · cited by 370
AddLeftStrictMonostatement and proof · cited by 203
Left.neg_neg_iffproof · cited by 16

Cited by3

Results whose statement or proof uses this declaration.

Real.Angle.toReal_piproof · cited by 9
neg_lt_selfproof · cited by 7
BoundedContinuousFunction.tietze_extension_stepproof · cited by 1