Theorems · Theorem · functional analysis
norm_natCast_eq_mul_norm_one
∀ (α : Type u_6) [inst : SeminormedRing α] [NormSMulClass ℤ α] (n : ℕ), ‖↑n‖ = ↑n * ‖1‖
- Defined in
- Mathlib.Analysis.Normed.Module.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedRingNormSMulClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 5,413
- SeminormedRingstatement and proof · cited by 446
- Int.cast_natCastproof · cited by 393
- NormSMulClassstatement and proof · cited by 107
- Nat.abs_castproof · cited by 36
- norm_intCast_eq_abs_mul_norm_oneproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- norm_natCastproof · cited by 2
- tendsto_natCast_atTop_coboundedproof · cited by 1