Theorems · Theorem · functional analysis
IsOfFinOrder.norm_eq_one
∀ {α : Type u_1} [inst : NormedRing α] [NormMulClass α] [NormOneClass α] {a : α}, IsOfFinOrder a → ‖a‖ = 1- Defined in
- Mathlib.Analysis.Normed.Ring.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- NormedRingstatement and proof · cited by 924
- norm_nonnegproof · cited by 725
- NormOneClassstatement and proof · cited by 136
- IsOfFinOrderstatement and proof · cited by 113
- NormMulClassstatement and proof · cited by 66
- MonoidWithZeroHom.toMonoidHomproof · cited by 39
- normHomproof · cited by 8
- MonoidHom.isOfFinOrderproof · cited by 6
- IsOfFinOrder.eq_oneproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddChar.norm_applyproof · cited by 2
- NumberField.Units.mem_torsionproof · cited by 2