Theorems · Theorem · order theory
mul_lt_mul_left_of_neg
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] [ExistsAddOfLE R] [PosMulStrictMono R]
[AddRightStrictMono R] [AddRightReflectLT R] {a b c : R}, c < 0 → (c * a < c * b ↔ b < a)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- LinearOrderstatement and proof · cited by 8,572
- ExistsAddOfLEstatement and proof · cited by 330
- AddRightStrictMonostatement and proof · cited by 160
- PosMulStrictMonostatement and proof · cited by 151
- AddRightReflectLTstatement and proof · cited by 29
- StrictAnti.lt_iff_gtproof · cited by 10
- strictAnti_mul_leftproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Function.Periodic.norm_qParam_lt_iffproof · cited by 1