Theorems · Theorem · order theory
mul_le_mul_iff_left
∀ {α : Type u_1} [inst : Mul α] [inst_1 : LE α] [MulLeftMono α] [MulLeftReflectLE α] (a : α) {b c : α},
a * b ≤ a * c ↔ b ≤ c- Cited by
- 15 results in Mathlib
- Foundations
- Depth 5 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.
- MulLeftMonostatement and proof · cited by 410
- CovariantClass.elimproof · cited by 22
- MulLeftReflectLEstatement and proof · cited by 13
- rel_iff_cov'proof · cited by 5
- MulLeftReflectLE.le_of_mul_le_mul_left'proof · cited by 2
Cited by15
Results whose statement or proof uses this declaration.
- inv_le_inv_iffproof · cited by 11
- inv_mul_le_iff_le_mulproof · cited by 5
- Left.one_le_inv_iffproof · cited by 4
- mul_inv_le_inv_mul_iffproof · cited by 3
- Left.inv_le_one_iffproof · cited by 3
- le_inv_mul_iff_mul_leproof · cited by 2
- div_le_div_iff_leftproof · cited by 1
- mul_le_iff_le_one_right'proof · cited by 0
- le_mul_iff_one_le_right'proof · cited by 0
- Set.Icc_mul_Iccproof · cited by 0
- Function.Injective.isOrderedCancelMonoidproof · cited by 0
- le_inv_iff_mul_le_one_leftproof · cited by 0