Theorems · Theorem · order theory
mul_le_mul_iff_of_pos_left
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [PosMulMono α] [PosMulReflectLE α],
0 < a → (a * b ≤ a * c ↔ b ≤ c)Alias of mul_le_mul_iff_right₀.
- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 8 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 · cited by 7,952
- PosMulMonostatement · cited by 165
- mul_le_mul_iff_right₀proof · cited by 38
- PosMulReflectLEstatement · cited by 16
Cited by13
Results whose statement or proof uses this declaration.
- inv_mul_le_iff₀proof · cited by 16
- le_inv_mul_iff₀proof · cited by 8
- Ideal.mul_iInfproof · cited by 3
- Real.circleAverage_monoproof · cited by 3
- Real.circleAverage_mono_on_of_le_circleproof · cited by 2
- Real.circleAverage_nonneg_of_nonnegproof · cited by 1
- IsMultiplyPretransitive.alternatingGroup_leproof · cited by 1
- Real.sum_ofDigitsTerm_digits_leproof · cited by 1
- Real.abs_circleAverage_le_circleAverage_absproof · cited by 1
- Real.norm_exp_I_mul_ofReal_sub_one_leproof · cited by 1
- HurwitzZeta.isBigO_atTop_cosKernel_subproof · cited by 0
- HurwitzZeta.isBigO_atTop_sinKernelproof · cited by 0