Theorems · Theorem · order theory
mul_lt_mul_of_neg_left
∀ {R : Type u} [inst : Semiring R] [inst_1 : PartialOrder R] {a b c : R} [ExistsAddOfLE R] [PosMulStrictMono R]
[AddRightStrictMono R] [AddRightReflectLT R], b < a → c < 0 → c * a < c * b- Cited by
- 5 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- PartialOrderstatement and proof · cited by 6,410
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- LT.lt.leproof · cited by 2,189
- MulZeroClass.zero_mulproof · cited by 1,625
- add_assocproof · cited by 746
- add_mulproof · cited by 363
- ExistsAddOfLEstatement and proof · cited by 330
- AddRightStrictMonostatement and proof · cited by 160
- PosMulStrictMonostatement and proof · cited by 151
- add_left_commproof · cited by 76
Cited by5
Results whose statement or proof uses this declaration.
- strictAnti_mul_leftproof · cited by 5
- Real.rpow_lt_rpow_of_exponent_gtproof · cited by 5
- geom_sum_alternating_of_lt_neg_oneproof · cited by 2
- mul_lt_of_one_lt_rightproof · cited by 0
- lt_mul_of_lt_one_rightproof · cited by 0