Theorems · Theorem · order theory
add_nonneg
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftMono α] {a b : α}, 0 ≤ a → 0 ≤ b → 0 ≤ a + bAlias of Left.add_nonneg.
- Cited by
- 104 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 30 definitions · uses no axioms
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.
- Preorderstatement · cited by 7,952
- AddZeroClassstatement · cited by 1,237
- AddLeftMonostatement · cited by 687
- Left.add_nonnegproof · cited by 3
Cited by104
Results whose statement or proof uses this declaration.
- zero_le_twoproof · cited by 44
- Complex.normSq_nonnegproof · cited by 14
- SameRay.norm_addproof · cited by 7
- MeasureTheory.integrable_of_le_of_leproof · cited by 6
- PointedCone.dual_hullproof · cited by 6
- convex_segmentproof · cited by 5
- HasFDerivAt.le_of_lip'proof · cited by 4
- MeasureTheory.measureReal_union_leproof · cited by 4
- Nat.floor_add_natCastproof · cited by 4
- Finset.convexHull_eqproof · cited by 4
- finsum_nonnegproof · cited by 4
- Function.locallyFinsuppWithin.logCounting_nonnegproof · cited by 3