Theorems · Theorem · functional analysis
Real.norm_of_nonpos
∀ {r : ℝ}, r ≤ 0 → ‖r‖ = -r- Defined in
- Mathlib.Analysis.Normed.Group.Real
- Cited by
- 4 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
- abs_of_nonposproof · cited by 53
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_eq_lintegral_pos_part_sub_lintegral_neg_partproof · cited by 2
- AkraBazziRecurrence.GrowsPolynomially.add_isLittleOproof · cited by 1
- ExistsContDiffBumpBase.y_pos_of_mem_ballproof · cited by 1
- NumberField.mixedEmbedding.negAt_signSet_apply_isRealproof · cited by 0