Theorems · Theorem · order theory
strictAnti_mul_left
∀ {R : Type u} [inst : Semiring R] [inst_1 : PartialOrder R] [ExistsAddOfLE R] [PosMulStrictMono R]
[AddRightStrictMono R] [AddRightReflectLT R] {a : R}, a < 0 → StrictAnti fun x => a * x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
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
- PartialOrderstatement and proof · cited by 6,410
- ExistsAddOfLEstatement and proof · cited by 330
- StrictAntistatement · cited by 204
- AddRightStrictMonostatement and proof · cited by 160
- PosMulStrictMonostatement and proof · cited by 151
- AddRightReflectLTstatement and proof · cited by 29
- mul_lt_mul_of_neg_leftproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- StrictMono.const_mul_of_negproof · cited by 1
- mul_lt_mul_left_of_negproof · cited by 1
- cmp_mul_neg_leftproof · cited by 0
- StrictAnti.const_mul_of_negproof · cited by 0
- mul_le_mul_left_of_negproof · cited by 0