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chore: don't expose the definition of nnnorm #37608

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14 changes: 9 additions & 5 deletions Mathlib/Analysis/Normed/Group/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -373,17 +373,21 @@ variable [FunLike 𝓕 E F]

section NNNorm

@[no_expose]
instance (priority := 100) SeminormedAddGroup.toNNNorm {E : Type*} [SeminormedAddGroup E] :
NNNorm E :=
⟨fun a => ⟨‖a‖, norm_nonneg a⟩⟩

-- See note [lower instance priority]
@[to_additive]
@[no_expose, to_additive existing]
instance (priority := 100) SeminormedGroup.toNNNorm : NNNorm E :=
⟨fun a => ⟨‖a‖, norm_nonneg' a⟩⟩

@[to_additive (attr := simp, norm_cast) coe_nnnorm]
theorem coe_nnnorm' (a : E) : (‖a‖₊ : ℝ) = ‖a‖ := rfl
theorem coe_nnnorm' (a : E) : (‖a‖₊ : ℝ) = ‖a‖ := by rfl

@[to_additive (attr := simp) coe_comp_nnnorm]
theorem coe_comp_nnnorm' : (toReal : ℝ≥0 → ℝ) ∘ (nnnorm : E → ℝ≥0) = norm :=
rfl
theorem coe_comp_nnnorm' : (toReal : ℝ≥0 → ℝ) ∘ (nnnorm : E → ℝ≥0) = norm := by rfl

@[to_additive (attr := simp) norm_toNNReal]
theorem norm_toNNReal' : ‖a‖.toNNReal = ‖a‖₊ :=
Expand Down Expand Up @@ -527,7 +531,7 @@ lemma nnnorm_div_eq_nnnorm_left (x : E) {y : E} (h : ‖y‖₊ = 0) : ‖x / y
/-- The nonnegative norm seen as an `ENNReal` and then as a `Real` is equal to the norm. -/
@[to_additive toReal_coe_nnnorm /-- The nonnegative norm seen as an `ENNReal` and
then as a `Real` is equal to the norm. -/]
theorem toReal_coe_nnnorm' (a : E) : (‖a‖₊ : ℝ≥0∞).toReal = ‖a‖ := rfl
theorem toReal_coe_nnnorm' (a : E) : (‖a‖₊ : ℝ≥0∞).toReal = ‖a‖ := by rfl

open scoped symmDiff in
@[to_additive]
Expand Down
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