Theorems · Theorem · order theory
mul_le_mul_of_nonneg_right
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [MulPosMono α],
b ≤ c → 0 ≤ a → b * a ≤ c * a- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 301 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 17 definitions · uses no axioms
- Assumes
- MulZeroPreorderMulPosMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- MulPosMonostatement and proof · cited by 128
- MulPosMono.mul_le_mul_of_nonneg_rightproof · cited by 1
Cited by301
Results whose statement or proof uses this declaration.
- div_le_div_of_nonneg_rightproof · cited by 77
- mul_le_of_le_one_leftproof · cited by 37
- mul_nonpos_of_nonpos_of_nonnegproof · cited by 24
- le_mul_of_one_le_leftproof · cited by 19
- ContinuousLinearMap.isBoundedBilinearMapproof · cited by 18
- mul_le_mul_of_nonpos_rightproof · cited by 13
- EReal.monotone_div_right_of_nonnegproof · cited by 11
- ProbabilityTheory.integrable_exp_mul_of_le_of_leproof · cited by 7
- IsLinearMap.with_boundproof · cited by 7
- mul_le_one₀proof · cited by 7
- ContinuousLinearMap.norm_smulRight_applyproof · cited by 6
- Asymptotics.IsBigOWith.weakenproof · cited by 5
Showing the 200 most cited of 301.