Theorems · Theorem · order theory
abs_abs
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] [AddRightMono α] (a : α), |(|a|)| = |a|- Cited by
- 19 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- absstatement · cited by 1,814
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- abs_of_nonnegproof · cited by 279
- abs_nonnegproof · cited by 168
Cited by19
Results whose statement or proof uses this declaration.
- Real.log_absproof · cited by 17
- MvPowerSeries.isRestricted_abs_iffproof · cited by 4
- ProbabilityTheory.integrable_rpow_mul_exp_of_integrable_exp_mulproof · cited by 3
- norm_abs_eq_normproof · cited by 2
- summable_jacobiTheta₂_term_fderiv_iffproof · cited by 2
- ArchimedeanClass.mk_absproof · cited by 2
- summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexpproof · cited by 2
- MeasureTheory.tendstoInDistribution_of_tendstoInMeasure_subproof · cited by 2
- ProbabilityTheory.integrable_rpow_abs_mul_exp_add_of_integrable_exp_mulproof · cited by 2
- UpperHalfPlane.IsZeroAtImInfty.slashproof · cited by 1
- comap_abs_nhds_zeroproof · cited by 1
- Convex.isLittleO_pow_succ_realproof · cited by 1