Theorems · Theorem · order theory
mul_le_mul_right_of_neg
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] [ExistsAddOfLE R] [MulPosStrictMono R] [AddRightMono R]
[AddRightReflectLE R] {a b c : R}, c < 0 → (a * c ≤ b * c ↔ b ≤ a)- Cited by
- 2 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
- AddRightMonostatement and proof · cited by 367
- ExistsAddOfLEstatement and proof · cited by 330
- MulPosStrictMonostatement and proof · cited by 94
- AddRightReflectLEstatement and proof · cited by 53
- StrictAnti.le_iff_geproof · cited by 16
- strictAnti_mul_rightproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Real.rpow_le_rpow_left_iff_of_base_lt_oneproof · cited by 4
- Matrix.det_ne_zero_of_sum_col_posproof · cited by 1