Theorems · Theorem · order theory
Left.add_nonneg
∀ {α : Type u_1} [inst : AddZeroClass α] [inst_1 : Preorder α] [AddLeftMono α] {a b : α}, 0 ≤ a → 0 ≤ b → 0 ≤ a + bAssumes left covariance.
The lemma assuming right covariance is Right.add_nonneg.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · 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 and proof · cited by 7,952
- AddZeroClassstatement and proof · cited by 1,237
- AddLeftMonostatement and proof · cited by 687
- le_add_of_le_of_nonnegproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- add_nonnegproof · cited by 104
- two_mul_le_add_of_sq_le_mulproof · cited by 2
- norm_add_eq_iff_realproof · cited by 0