Theorems · Theorem · order theory
mul_le_mul
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c d : α} [PosMulMono α] [MulPosMono α],
a ≤ b → c ≤ d → 0 ≤ c → 0 ≤ b → a * c ≤ b * dAlias of mul_le_mul_of_nonneg'.
- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 144 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 18 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
- PosMulMonostatement · cited by 165
- MulPosMonostatement · cited by 128
- mul_le_mul_of_nonneg'proof · cited by 1
Cited by144
Results whose statement or proof uses this declaration.
- div_le_div₀proof · cited by 53
- Finset.prod_le_prodproof · cited by 40
- Function.hasTemperateGrowth_one_add_norm_sq_rpowproof · cited by 9
- norm_jacobiTheta₂_term_leproof · cited by 5
- PhragmenLindelof.isBigO_sub_exp_rpowproof · cited by 5
- MeasureTheory.DominatedFinMeasAdditive.smulproof · cited by 5
- ContinuousLinearMap.le_of_opNorm_le_of_leproof · cited by 4
- PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExceptproof · cited by 4
- NNReal.summable_and_Lr_rpow_le_Lp_mul_Lq_tsumproof · cited by 4
- GenContFract.fib_le_of_contsAux_bproof · cited by 4
- mul_self_le_mul_selfproof · cited by 4
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4