Theorems · Theorem · functional analysis
Real.le_norm_self
∀ (r : ℝ), r ≤ ‖r‖
- Defined in
- Mathlib.Analysis.Normed.Group.Real
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement · cited by 5,413
- le_abs_selfproof · cited by 113
Cited by16
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.le_algebraMap_norm_selfproof · cited by 7
- CStarAlgebra.norm_le_iff_le_algebraMapproof · cited by 5
- tendsto_tsum_of_dominated_convergenceproof · cited by 2
- Memℓp.monoproof · cited by 2
- spectrum.le_nnnorm_of_memproof · cited by 2
- MeasureTheory.measureReal_abs_gt_le_integral_charFunproof · cited by 2
- eventually_norm_symmL_trivializationAt_comp_self_ltproof · cited by 1
- eventually_norm_symmL_trivializationAt_self_comp_ltproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_add_smoothingFn_geproof · cited by 1
- AkraBazziRecurrence.rpow_p_mul_one_sub_smoothingFn_leproof · cited by 1
- LSeries_eq_mul_integral'proof · cited by 1
- FormalMultilinearSeries.radius_prod_eq_minproof · cited by 1