Theorems · Theorem · order theory
negPart_of_nonpos
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] {a : α} [AddLeftMono α], a ≤ 0 → a⁻ = -aAlias of the reverse direction of negPart_eq_neg.
- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- LatticeAddGroupAddLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- NegPart.negPartstatement · cited by 107
- negPart_eq_negproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- CFC.posPart_sub_negPartproof · cited by 10
- CFC.posPart_add_negPartproof · cited by 2
- ValueDistribution.logCounting_constproof · cited by 1
- MeromorphicOn.negPart_divisor_add_le_maxproof · cited by 1
- spectrum_star_mul_self_nonnegproof · cited by 1
- CFC.negPart_mul_posPartproof · cited by 1
- IsSelfAdjoint.norm_eq_max_norm_posPart_negPartproof · cited by 0
- CFC.posPart_mul_negPartproof · cited by 0
- CFC.negPart_algebraMapproof · cited by 0
- Function.locallyFinsuppWithin.restrict_negPartproof · cited by 0
- CFC.negPart_oneproof · cited by 0