Theorems · Theorem · order theory
div_lt_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
- 38 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_lt_iff₀proof · cited by 45
Cited by38
Results whose statement or proof uses this declaration.
- isLittleO_pow_pow_of_lt_leftproof · cited by 5
- Complex.arg_le_pi_div_two_iffproof · cited by 4
- norm_add_lt_of_not_sameRayproof · cited by 3
- exists_dist_lt_ltproof · cited by 3
- Affine.Simplex.sOppSide_affineSpan_faceOpposite_of_pos_of_negproof · cited by 3
- ZMod.toAddCircle_injectiveproof · cited by 3
- Int.fract_div_natCast_eq_div_natCast_modproof · cited by 3
- FormalMultilinearSeries.isLittleO_of_lt_radiusproof · cited by 3
- Frullani.tendsto_integral_inv_smul_of_tendsto_uniformproof · cited by 2
- hasSum_two_pi_I_cauchyPowerSeries_integralproof · cited by 2
- one_div_lt_one_div_of_ltproof · cited by 2
- Complex.neg_pi_div_two_le_arg_iffproof · cited by 2