Theorems · Theorem · functional analysis
CStarRing.norm_one
∀ {E : Type u_2} [inst : NormedRing E] [inst_1 : StarRing E] [CStarRing E] [Nontrivial E], ‖1‖ = 1- Defined in
- Mathlib.Analysis.CStarAlgebra.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Nontrivialstatement and proof · cited by 2,416
- StarRingstatement and proof · cited by 1,686
- LT.lt.ne'proof · cited by 1,417
- Star.starproof · cited by 1,082
- NormedRingstatement and proof · cited by 924
- one_ne_zeroproof · cited by 885
- norm_pos_iffproof · cited by 168
- CStarRingstatement and proof · cited by 61
Cited by3
Results whose statement or proof uses this declaration.
- CStarRing.norm_coe_unitaryproof · cited by 2
- MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closedproof · cited by 2
- UnitAddTorus.mFourier_normproof · cited by 1