Theorems · Theorem · order theory
lt_of_mul_lt_mul_right
∀ {α : Type u_1} [inst : Mul α] [inst_1 : Zero α] [inst_2 : Preorder α] {a b c : α} [MulPosReflectLT α],
b * a < c * a → 0 ≤ a → b < c- Defined in
- Mathlib.Algebra.Order.GroupWithZero.Defs
- Cited by
- 8 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
- MulPosReflectLTstatement and proof · cited by 93
- ContravariantClass.elimproof · cited by 12
Cited by8
Results whose statement or proof uses this declaration.
- mul_lt_mul_iff_left₀proof · cited by 13
- pos_of_mul_pos_leftproof · cited by 11
- Right.inv_posproof · cited by 3
- SimpleGraph.FarFromTriangleFree.lt_halfproof · cited by 1
- MulPosReflectLT.toMulPosMonoproof · cited by 1
- MulPosReflectLT.toMulPosStrictMonoproof · cited by 0
- one_lt_of_lt_mul_right₀proof · cited by 0
- lt_of_mul_lt_mul_of_nonneg_rightproof · cited by 0