Theorems · Theorem · order theory
div_nonneg
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] {a b : G₀},
0 ≤ a → 0 ≤ b → 0 ≤ a / b- Cited by
- 103 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 188 definitions · 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.
- PartialOrderstatement and proof · cited by 6,410
- div_eq_mul_invproof · cited by 715
- GroupWithZerostatement and proof · cited by 691
- mul_nonnegproof · cited by 397
- PosMulReflectLTstatement and proof · cited by 278
- inv_nonnegproof · cited by 56
Cited by103
Results whose statement or proof uses this declaration.
- Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_posproof · cited by 58
- Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonnegproof · cited by 29
- EuclideanGeometry.angle_eq_pi_iff_sbtwproof · cited by 6
- NNRat.cast_nonnegproof · cited by 6
- isLittleO_pow_pow_of_lt_leftproof · cited by 5
- Real.sqrtTwoAddSeries_step_upproof · cited by 5
- InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zeroproof · cited by 5
- Real.pi_upper_bound_startproof · cited by 5
- InnerProductGeometry.cos_angle_add_of_inner_eq_zeroproof · cited by 5
- InnerProductGeometry.sin_angle_add_of_inner_eq_zeroproof · cited by 5
- AkraBazziRecurrence.eventually_bi_mul_le_rproof · cited by 4
- NumberField.hermiteTheorem.rank_le_rankOfDiscrBddproof · cited by 4