Theorems · Theorem · order theory
one_le_div
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a b : α},
0 < b → (1 ≤ a / b ↔ b ≤ a)- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 19 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
- le_div_iff₀proof · cited by 75
Cited by19
Results whose statement or proof uses this declaration.
- Stirling.log_stirlingSeq_sdiff_leproof · cited by 3
- NumberField.abs_discr_geproof · cited by 2
- LSeries.tendsto_cpow_mul_atTopproof · cited by 2
- Chebyshev.abs_psi_sub_theta_le_sqrt_mul_logproof · cited by 2
- NNReal.rpow_add_rpow_leproof · cited by 2
- Behrend.ceil_lt_mulproof · cited by 1
- Behrend.div_lt_floorproof · cited by 1
- MeasureTheory.StronglyMeasurable.norm_approxBounded_leproof · cited by 1
- mul_pow_le_nat_floor_powproof · cited by 1
- schnirelmannDensity_eq_one_iffproof · cited by 1
- ENNReal.lintegral_Lp_add_le_of_le_oneproof · cited by 1
- ContinuousOn.isBigOWith_rev_principalproof · cited by 1