Theorems · Theorem · order theory
posPart_nonneg
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : SubNegMonoid α] (a : α), 0 ≤ a⁺- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- 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
- le_sup_rightproof · cited by 242
- PosPart.posPartstatement · cited by 113
- SubNegMonoidstatement and proof · cited by 79
Cited by8
Results whose statement or proof uses this declaration.
- CFC.posPart_nonnegproof · cited by 5
- ValueDistribution.logCounting_nonnegproof · cited by 2
- MeasureTheory.mul_integral_upcrossingsBefore_le_integral_pos_part_auxproof · cited by 1
- ValueDistribution.logCounting_monotoneOnproof · cited by 1
- ValueDistribution.Cartan.integrable_integral_norm_cartanKernelproof · cited by 1
- posPart_pos_iffproof · cited by 0