Theorems · Theorem · order theory
Left.mul_nonneg
∀ {α : Type u_1} [inst : MulZeroClass α] {a b : α} [inst_1 : Preorder α] [PosMulMono α], 0 ≤ a → 0 ≤ b → 0 ≤ a * bAssumes left covariance.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_le_mul_of_nonneg_leftproof · cited by 361
- MulZeroClassstatement and proof · cited by 232
- PosMulMonostatement and proof · cited by 165
Cited by6
Results whose statement or proof uses this declaration.
- mul_nonnegproof · cited by 397
- Left.neg_of_mul_neg_leftproof · cited by 1
- Left.neg_of_mul_neg_rightproof · cited by 1
- Matrix.nonneg_mulVec_of_mem_rowStochasticproof · cited by 0
- Matrix.nonneg_vecMul_of_mem_colStochasticproof · cited by 0
- Matrix.nonneg_mulVec_of_mem_colStochasticproof · cited by 0