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docs: replace ⬝ BLACK VERY SMALL SQUARE with · MIDDLE DOT (#6522)
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`MIDDLE DOT` is now valid Lean syntax for function arguments, which is what these docstrings are referring to.
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eric-wieser committed Aug 11, 2023
1 parent cf85b04 commit 30b7080
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Showing 3 changed files with 4 additions and 4 deletions.
4 changes: 2 additions & 2 deletions Mathlib/Analysis/Normed/Group/Basic.lean
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Expand Up @@ -494,14 +494,14 @@ open Lean Meta Qq Function
`norm_nonneg'`. -/
@[positivity Norm.norm _]
def evalMulNorm : PositivityExt where eval {_ _} _zα _pα e := do
let .app _ a ← whnfR e | throwError "not ‖ ‖"
let .app _ a ← whnfR e | throwError "not ‖ · ‖"
let p ← mkAppM ``norm_nonneg' #[a]
pure (.nonnegative p)

/-- Extension for the `positivity` tactic: additive norms are nonnegative, via `norm_nonneg`. -/
@[positivity Norm.norm _]
def evalAddNorm : PositivityExt where eval {_ _} _zα _pα e := do
let .app _ a ← whnfR e | throwError "not ‖ ‖"
let .app _ a ← whnfR e | throwError "not ‖ · ‖"
let p ← mkAppM ``norm_nonneg #[a]
pure (.nonnegative p)

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2 changes: 1 addition & 1 deletion Mathlib/Analysis/NormedSpace/BanachSteinhaus.lean
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Expand Up @@ -75,7 +75,7 @@ open ENNReal

open ENNReal

/-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖‖₊ : ℝ≥0∞`
/-- This version of Banach-Steinhaus is stated in terms of suprema of `↑‖·‖₊ : ℝ≥0∞`
for convenience. -/
theorem banach_steinhaus_iSup_nnnorm {ι : Type*} [CompleteSpace E] {g : ι → E →SL[σ₁₂] F}
(h : ∀ x, ⨆ i, ↑‖g i x‖₊ < ∞) : ⨆ i, ↑‖g i‖₊ < ∞ := by
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2 changes: 1 addition & 1 deletion Mathlib/Analysis/NormedSpace/Spectrum.lean
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Expand Up @@ -47,7 +47,7 @@ This file contains the basic theory for the resolvent and spectrum of a Banach a

open scoped ENNReal NNReal

/-- The *spectral radius* is the supremum of the `nnnorm` (`‖‖₊`) of elements in the spectrum,
/-- The *spectral radius* is the supremum of the `nnnorm` (`‖·‖₊`) of elements in the spectrum,
coerced into an element of `ℝ≥0∞`. Note that it is possible for `spectrum 𝕜 a = ∅`. In this
case, `spectralRadius a = 0`. It is also possible that `spectrum 𝕜 a` be unbounded (though
not for Banach algebras, see `spectrum.is_bounded`, below). In this case,
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