Theorems · Theorem · order theory
neg_lt_self
∀ {α : Type u} [inst : AddGroup α] [inst_1 : Preorder α] [AddLeftStrictMono α] {a : α}, 0 < a → -a < aAlias of Left.neg_lt_self.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
- AddGroupstatement · cited by 4,410
- AddLeftStrictMonostatement · cited by 203
- Left.neg_lt_selfproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- PhragmenLindelof.horizontal_stripproof · cited by 3
- Real.differentiableWithinAt_arcsin_Iciproof · cited by 2
- Real.neg_pi_div_two_lt_arcsinproof · cited by 2
- Real.surjOn_tanproof · cited by 2
- Real.arcsin_lt_pi_div_twoproof · cited by 2
- Real.tendsto_cos_neg_pi_div_twoproof · cited by 1
- Real.tendsto_cos_pi_div_twoproof · cited by 1