Theorems · Theorem · order theory
MulLECancellable.mul_le_mul_iff_left
∀ {α : Type u_1} [inst : LE α] [inst_1 : Mul α] [MulLeftMono α] {a b c : α},
MulLECancellable a → (a * b ≤ a * c ↔ b ≤ c)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- LEMulMulLeftMono
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.
- MulLeftMonostatement and proof · cited by 410
- mul_le_mul_rightproof · cited by 47
- MulLECancellablestatement and proof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- MulLECancellable.le_mul_iff_one_le_rightproof · cited by 1
- MulLECancellable.mul_le_iff_le_one_rightproof · cited by 1
- MulLECancellable.mul_le_mul_iff_rightproof · cited by 0