Theorems · Theorem · order theory
div_le_one
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a b : α},
0 < b → (a / b ≤ 1 ↔ a ≤ b)- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 45 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
- one_mulproof · cited by 2,841
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- div_le_iff₀proof · cited by 97
Cited by29
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_eq_pi_iff_sbtwproof · cited by 6
- Real.mul_le_sinproof · cited by 4
- Urysohns.CU.approx_le_oneproof · cited by 4
- EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eqproof · cited by 4
- ContDiffBump.one_of_mem_closedBallproof · cited by 4
- Pell.exists_of_not_isSquareproof · cited by 3
- MeasureTheory.tendsto_Lp_finite_of_tendsto_ae_of_measproof · cited by 1
- Real.smoothTransition.le_oneproof · cited by 1
- MeasureTheory.StronglyMeasurable.norm_approxBounded_leproof · cited by 1
- tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_supportproof · cited by 1
- tendsto_integral_mul_one_add_inv_smul_sq_powproof · cited by 1