Theorems · Theorem · functional analysis
AddCircle.norm_eq_of_zero
∀ {x : ℝ}, ‖↑x‖ = |x|- Defined in
- Mathlib.Analysis.Normed.Group.AddCircle
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Set.ofPredproof · cited by 6,101
- Norm.normstatement · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- Set.extproof · cited by 2,266
- absstatement and proof · cited by 1,814
- AddSubgroup.zmultiplesstatement · cited by 493
- QuotientAddGroup.mkstatement and proof · cited by 348
- Metric.infDistproof · cited by 68
- dist_zeroproof · cited by 16
- AddSubgroup.zmultiples_zero_eq_botproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddCircle.norm_eqproof · cited by 6
- AddCircle.coe_real_preimage_closedBall_period_zeroproof · cited by 2