@@ -662,24 +662,6 @@ variable (K) in
662662lemma nnnorm_nsmul [NormedAddCommGroup E] [NormedSpace K E] (n : ℕ) (x : E) :
663663 ‖n • x‖₊ = n • ‖x‖₊ := by simpa [Nat.cast_smul_eq_nsmul] using nnnorm_smul (n : K) x
664664
665- section NormedField
666- variable [NormedField E] [CharZero E] [NormedSpace K E]
667- include K
668-
669- variable (K) in
670- lemma norm_nnqsmul (q : ℚ≥0 ) (x : E) : ‖q • x‖ = q • ‖x‖ := by
671- simpa [NNRat.cast_smul_eq_nnqsmul] using norm_smul (q : K) x
672-
673- variable (K) in
674- lemma nnnorm_nnqsmul (q : ℚ≥0 ) (x : E) : ‖q • x‖₊ = q • ‖x‖₊ := by
675- simpa [NNRat.cast_smul_eq_nnqsmul] using nnnorm_smul (q : K) x
676-
677- @[bound]
678- lemma norm_expect_le {ι : Type *} {s : Finset ι} {f : ι → E} : ‖𝔼 i ∈ s, f i‖ ≤ 𝔼 i ∈ s, ‖f i‖ :=
679- Finset.le_expect_of_subadditive norm_zero norm_add_le fun _ _ ↦ by rw [norm_nnqsmul K]
680-
681- end NormedField
682-
683665theorem mul_self_norm (z : K) : ‖z‖ * ‖z‖ = normSq z := by rw [normSq_eq_def', sq]
684666
685667attribute [rclike_simps] norm_zero norm_one norm_eq_zero abs_norm norm_inv norm_div
@@ -788,6 +770,24 @@ end Instances
788770
789771namespace RCLike
790772
773+ section NormedField
774+ variable [NormedField E] [CharZero E] [NormedSpace K E]
775+ include K
776+
777+ variable (K) in
778+ lemma norm_nnqsmul (q : ℚ≥0 ) (x : E) : ‖q • x‖ = q • ‖x‖ := by
779+ simpa [NNRat.cast_smul_eq_nnqsmul] using norm_smul (q : K) x
780+
781+ variable (K) in
782+ lemma nnnorm_nnqsmul (q : ℚ≥0 ) (x : E) : ‖q • x‖₊ = q • ‖x‖₊ := by
783+ simpa [NNRat.cast_smul_eq_nnqsmul] using nnnorm_smul (q : K) x
784+
785+ @[bound]
786+ lemma norm_expect_le {ι : Type *} {s : Finset ι} {f : ι → E} : ‖𝔼 i ∈ s, f i‖ ≤ 𝔼 i ∈ s, ‖f i‖ :=
787+ Finset.le_expect_of_subadditive norm_zero norm_add_le fun _ _ ↦ by rw [norm_nnqsmul K]
788+
789+ end NormedField
790+
791791section Order
792792
793793open scoped ComplexOrder
0 commit comments