Theorems · Theorem · order theory
abs_inv
∀ {α : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] (a : α), |a⁻¹| = |a|⁻¹- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 35 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_inv₀proof · cited by 106
- absHomproof · cited by 5
Cited by35
Results whose statement or proof uses this declaration.
- Real.log_invproof · cited by 35
- ContDiffBump.support_eqproof · cited by 8
- IntervalIntegrable.comp_mul_leftproof · cited by 6
- AddCircle.norm_eqproof · cited by 6
- Affine.Simplex.exsphere_reindexproof · cited by 5
- ProbabilityTheory.gaussianReal_map_const_mulproof · cited by 4
- ContDiffBump.one_of_mem_closedBallproof · cited by 4
- Affine.Simplex.ExcenterExists.excenter_mapproof · cited by 3
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- MeasureTheory.Measure.integral_comp_smulproof · cited by 3
- Affine.Simplex.exsphere_complproof · cited by 3
- AkraBazziRecurrence.GrowsPolynomially.invproof · cited by 3