Theorems · Theorem · order theory
div_nonpos_of_nonneg_of_nonpos
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : LinearOrder G₀] {a b : G₀} [PosMulMono G₀],
0 ≤ a → b ≤ 0 → a / b ≤ 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
- PosMulMonostatement and proof · cited by 165
- mul_nonpos_of_nonneg_of_nonposproof · cited by 21
- inv_nonposproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Fernique.lt_normThreshold_zeroproof · cited by 2
- integral_gaussianproof · cited by 2
- BoxIntegral.Box.distortion_eq_of_sub_eq_divproof · cited by 1
- SimpleGraph.triangleRemovalBound_nonposproof · cited by 1
- integral_gaussian_Ioiproof · cited by 1
- HurwitzZeta.evenKernel_functional_equationproof · cited by 0