Theorems · Theorem · order theory
mul_nonneg_iff_of_pos_right
∀ {R : Type u} [inst : Semiring R] [inst_1 : LinearOrder R] {b c : R} [MulPosStrictMono R], 0 < c → (0 ≤ b * c ↔ 0 ≤ b)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- MulZeroClass.zero_mulproof · cited by 1,625
- MulPosStrictMonostatement and proof · cited by 94
- mul_le_mul_iff_left₀proof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- Int.fract_div_mul_self_mem_Icoproof · cited by 2
- NormedAddCommGroup.cauchy_series_of_le_geometric''proof · cited by 1
- wbtw_iff_of_leproof · cited by 1
- Fermat42.not_minimalproof · cited by 1
- eigenvalue_nonneg_of_nonnegproof · cited by 0