Theorems · Theorem · functional analysis
RCLike.norm_nsmul
∀ (K : Type u_1) {E : Type u_2} [inst : RCLike K] [inst_1 : NormedAddCommGroup E] [NormedSpace K E] (n : ℕ) (x : E),
‖n • x‖ = n • ‖x‖- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- RCLikestatement and proof · cited by 2,829
- nsmul_eq_mulproof · cited by 369
- norm_smulproof · cited by 242
- Nat.cast_smul_eq_nsmulproof · cited by 110
- RCLike.norm_natCastproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- InnerProductSpaceable.inner_.norm_sqproof · cited by 1
- Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_leproof · cited by 0