Theorems · Theorem · functional analysis
AddCircle.norm_eq
∀ (p : ℝ) {x : ℝ}, ‖↑x‖ = |x - ↑(round (p⁻¹ * x)) * p|- Defined in
- Mathlib.Analysis.Normed.Group.AddCircle
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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 and proof · cited by 5,413
- Set.rangeproof · cited by 4,705
- mul_oneproof · cited by 3,885
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- absstatement and proof · cited by 1,814
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- sub_zeroproof · cited by 938
Cited by6
Results whose statement or proof uses this declaration.
- AddCircle.norm_le_half_periodproof · cited by 2
- AddCircle.norm_eq'proof · cited by 1
- AddCircle.coe_real_preimage_closedBall_eq_iUnionproof · cited by 1
- AddCircle.norm_half_period_eqproof · cited by 1
- AddCircle.norm_coe_eq_abs_iffproof · cited by 0
- UnitAddCircle.norm_eqproof · cited by 0