Theorems · Theorem · order theory
abs_div
∀ {α : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] (a b : α), |a / b| = |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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absstatement · cited by 1,814
- map_div₀proof · cited by 98
- absHomproof · cited by 5
Cited by38
Results whose statement or proof uses this declaration.
- Real.log_divproof · cited by 21
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- abs_real_inner_div_norm_mul_norm_le_oneproof · cited by 4
- Real.abs_sinc_le_oneproof · cited by 3
- Liouville.irrationalproof · cited by 3
- Pell.exists_of_not_isSquareproof · cited by 3
- UpperHalfPlane.tendsto_smul_atImInftyproof · cited by 2
- CircleDeg1Lift.transnumAuxSeq_dist_ltproof · cited by 2
- GenContFract.abs_sub_convs_leproof · cited by 2
- ContinuousLinearMap.rayleighQuotient_le_normproof · cited by 2
- setOfPred_liouvilleWith_subset_auxproof · cited by 2
- EuclideanGeometry.angle_eq_angle_div_two_of_oangle_eq_of_sSameSideproof · cited by 2