Theorems · Theorem · order theory
mul_le_mul_iff_of_pos_right
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [MulPosMono α] [MulPosReflectLE α],
0 < a → (b * a ≤ c * a ↔ b ≤ c)Alias of mul_le_mul_iff_left₀.
- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 11 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
- MulPosMonostatement · cited by 128
- mul_le_mul_iff_left₀proof · cited by 19
- MulPosReflectLEstatement · cited by 17
Cited by11
Results whose statement or proof uses this declaration.
- mul_inv_le_iff₀proof · cited by 10
- le_mul_inv_iff₀proof · cited by 7
- HurwitzKernelBounds.summable_f_natproof · cited by 5
- Int.mul_cast_floor_div_cancel_of_posproof · cited by 3
- Nat.mul_cast_floor_div_cancelproof · cited by 2
- MvPolynomial.exists_mem_support_not_dvd_of_forall_totalDegree_leproof · cited by 1
- Complex.cos_ne_zero_of_arctan_boundsproof · cited by 1
- ContinuousLinearMap.norm_sndproof · cited by 0
- HurwitzZeta.isBigO_atTop_sinKernelproof · cited by 0
- HomogeneousLocalization.Away.finiteTypeproof · cited by 0
- ContinuousLinearMap.norm_fstproof · cited by 0