Theorems · Theorem · order theory
posPart_eq_self
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : SubNegMonoid α] {a : α}, a⁺ = a ↔ 0 ≤ a- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- LatticeSubNegMonoid
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.
- Latticestatement and proof · cited by 916
- PosPart.posPartstatement · cited by 113
- SubNegMonoidstatement and proof · cited by 79
- sup_eq_leftproof · cited by 71
Cited by6
Results whose statement or proof uses this declaration.
- posPart_of_nonnegproof · cited by 2
- MeasureTheory.Submartingale.upcrossings_ae_lt_top'proof · cited by 1
- MeasureTheory.crossing_pos_eqproof · cited by 1
- posPart_eq_of_posPart_posproof · cited by 1
- posPart_posproof · cited by 0
- IsSelfAdjoint.norm_eq_max_norm_posPart_negPartproof · cited by 0