Theorems · Theorem · order theory
Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos
∀ {α : Type u_4} [inst : GroupWithZero α] [inst_1 : PartialOrder α] {a b : α} [PosMulReflectLT α],
0 ≤ a → 0 < b → 0 ≤ a / b- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 23 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.
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.leproof · cited by 2,189
- GroupWithZerostatement and proof · cited by 691
- PosMulReflectLTstatement and proof · cited by 278
- div_nonnegproof · cited by 103
Cited by58
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.norm_smulRight_applyproof · cited by 6
- Real.sum_le_exp_of_nonnegproof · cited by 5
- EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eqproof · cited by 4
- Polynomial.Chebyshev.abs_eval_T_real_eq_one_iffproof · cited by 3
- UpperHalfPlane.cosh_half_distproof · cited by 3
- HasFPowerSeriesWithinOnBall.uniform_geometric_approx'proof · cited by 3
- Int.fract_div_natCast_eq_div_natCast_modproof · cited by 3
- FormalMultilinearSeries.isLittleO_of_lt_radiusproof · cited by 3
- ZMod.toAddCircle_injectiveproof · cited by 3
- ProbabilityTheory.Kernel.HasSubgaussianMGF.cgf_leproof · cited by 2
- ZetaAsymptotics.termTSum_of_ltproof · cited by 2
- ODE.FunSpace.dist_iterate_next_iterate_next_leproof · cited by 2