Theorems · Theorem · order theory
mul_lt_mul_iff_of_pos_right
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [MulPosStrictMono α]
[MulPosReflectLT α], 0 < a → (b * a < c * a ↔ b < c)Alias of mul_lt_mul_iff_left₀.
- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 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
- MulPosStrictMonostatement · cited by 94
- MulPosReflectLTstatement · cited by 93
- mul_lt_mul_iff_left₀proof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- mul_inv_lt_iff₀proof · cited by 8
- lt_mul_inv_iff₀proof · cited by 3
- Nat.lt_ratSqrt_add_inv_prec_sqproof · cited by 1
- Complex.cos_ne_zero_of_arctan_boundsproof · cited by 1