Theorems · Theorem · order theory
mul_le_mul_left
∀ {α : Type u_1} [inst : Mul α] [inst_1 : LE α] [i : MulRightMono α] {b c : α}, b ≤ c → ∀ (a : α), b * a ≤ c * a- Cited by
- 31 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- MulLEMulRightMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulRightMonostatement and proof · cited by 263
- CovariantClass.elimproof · cited by 22
Cited by31
Results whose statement or proof uses this declaration.
- mul_le_mul'proof · cited by 274
- le_mul_of_one_le_left'proof · cited by 15
- mul_lt_mul_of_le_of_ltproof · cited by 15
- mul_left_monoproof · cited by 10
- Cardinal.mul_eq_maxproof · cited by 8
- CanonicallyOrderedMul.toIsOrderedMonoidproof · cited by 5
- le_mul_of_one_le_of_leproof · cited by 4
- mul_le_of_le_one_left'proof · cited by 4
- Cardinal.add_eq_selfproof · cited by 4
- DoubleCentralizer.norm_fst_eq_sndproof · cited by 3
- Cardinal.le_mul_leftproof · cited by 3
- mul_lt_of_le_one_of_ltproof · cited by 3