Theorems · Theorem · order theory
posPart_of_nonneg
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : SubNegMonoid α] {a : α}, 0 ≤ a → a⁺ = aAlias of the reverse direction of posPart_eq_self.
- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 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
- posPart_eq_selfproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- CFC.posPart_algebraMap_nnrealproof · cited by 1
- CFC.posPart_oneproof · cited by 0