Theorems · Theorem · order theory
mul_lt_mul_of_pos_right
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [MulPosStrictMono α],
b < c → 0 < a → b * a < c * a- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 54 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- MulPosStrictMonostatement and proof · cited by 94
- MulPosStrictMono.mul_lt_mul_of_pos_rightproof · cited by 1
Cited by54
Results whose statement or proof uses this declaration.
- div_lt_div_of_pos_rightproof · cited by 16
- MeasureTheory.lintegral_iSupproof · cited by 16
- mul_lt_mul_iff_left₀proof · cited by 13
- mul_neg_of_neg_of_posproof · cited by 13
- Real.rpow_lt_rpowproof · cited by 12
- Polynomial.coeff_comp_degree_mul_degreeproof · cited by 7
- mul_lt_of_lt_one_leftproof · cited by 7
- mul_lt_mul_of_neg_rightproof · cited by 6
- Complex.canonicalFactor_ne_zeroproof · cited by 6
- lt_mul_of_one_lt_leftproof · cited by 5
- EuclideanGeometry.inner_pos_or_eq_of_dist_le_radiusproof · cited by 3
- mul_lt_mul_of_lt_of_le_of_nonneg_of_posproof · cited by 3