Theorems · Theorem · order theory
negPart_eq_neg
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] {a : α} [AddLeftMono α], a⁻ = -a ↔ a ≤ 0- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- LatticeAddGroupAddLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- sup_eq_leftproof · cited by 71
- Left.nonneg_neg_iffproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- negPart_of_nonposproof · cited by 11
- negPart_posproof · cited by 0
- IsSelfAdjoint.norm_eq_max_norm_posPart_negPartproof · cited by 0