Theorems · Theorem · order theory
mul_lt_mul_of_neg_right
∀ {R : Type u} [inst : Semiring R] [inst_1 : PartialOrder R] {a b c : R} [ExistsAddOfLE R] [MulPosStrictMono R]
[AddRightStrictMono R] [AddRightReflectLT R], b < a → c < 0 → a * c < b * c- Cited by
- 6 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.mul_zeroproof · cited by 2,091
- add_assocproof · cited by 746
- mul_addproof · cited by 413
- ExistsAddOfLEstatement and proof · cited by 330
- AddRightStrictMonostatement and proof · cited by 160
- MulPosStrictMonostatement and proof · cited by 94
- add_left_commproof · cited by 76
Cited by6
Results whose statement or proof uses this declaration.
- mul_pos_of_neg_of_negproof · cited by 40
- div_lt_iff_of_negproof · cited by 7
- strictAnti_mul_rightproof · cited by 5
- mul_lt_of_one_lt_leftproof · cited by 1
- lt_mul_of_lt_one_leftproof · cited by 1
- div_lt_div_of_neg_of_ltproof · cited by 0