diff --git a/Archive/Imo/Imo2024Q3.lean b/Archive/Imo/Imo2024Q3.lean
index 6813f53bfd96b2..0fd39443836125 100644
--- a/Archive/Imo/Imo2024Q3.lean
+++ b/Archive/Imo/Imo2024Q3.lean
@@ -941,8 +941,6 @@ lemma exists_a_apply_add_eq : ∃ b c, 0 < c ∧ ∀ n, b < n →
     rcases hc.even_p (by lia) (hs n) with ⟨_, ht⟩
     simp [ht, ← two_mul]
 
-variable {a N}
-
 end Condition
 
 theorem result {a : ℕ → ℕ} {N : ℕ} (h : Condition a N) :
diff --git a/Mathlib.lean b/Mathlib.lean
index db27eeb4f4fb22..0203d4af567c1c 100644
--- a/Mathlib.lean
+++ b/Mathlib.lean
@@ -6684,6 +6684,7 @@ public import Mathlib.Tactic.Linter.EmptyLine
 public import Mathlib.Tactic.Linter.FindDeprecations
 public import Mathlib.Tactic.Linter.FlexibleLinter
 public import Mathlib.Tactic.Linter.GlobalAttributeIn
+public import Mathlib.Tactic.Linter.GlobalSyntax
 public import Mathlib.Tactic.Linter.HashCommandLinter
 public import Mathlib.Tactic.Linter.HaveLetLinter
 public import Mathlib.Tactic.Linter.Header
diff --git a/Mathlib/Data/ENNReal/Basic.lean b/Mathlib/Data/ENNReal/Basic.lean
index 2691e09c44add8..66b08e226428fd 100644
--- a/Mathlib/Data/ENNReal/Basic.lean
+++ b/Mathlib/Data/ENNReal/Basic.lean
@@ -679,6 +679,7 @@ lemma iInf_coe_lt_top : ⨅ i, (f i : ℝ≥0∞) < ⊤ ↔ Nonempty ι := WithT
 end CompleteLattice
 
 section Bit
+set_option linter.globalSyntax true -- Prevents the flagging of the enclosing `section`/`end` pair.
 
 -- TODO: add lemmas about `OfNat.ofNat`
 
diff --git a/Mathlib/Init.lean b/Mathlib/Init.lean
index 6e556ef2b17c94..5eaaf7e3ab2d87 100644
--- a/Mathlib/Init.lean
+++ b/Mathlib/Init.lean
@@ -9,6 +9,7 @@ public import Mathlib.Tactic.Linter.DocPrime
 public import Mathlib.Tactic.Linter.DocString
 public import Mathlib.Tactic.Linter.EmptyLine
 public import Mathlib.Tactic.Linter.GlobalAttributeIn
+public import Mathlib.Tactic.Linter.GlobalSyntax
 public import Mathlib.Tactic.Linter.HashCommandLinter
 public import Mathlib.Tactic.Linter.Header
 public import Mathlib.Tactic.Linter.FlexibleLinter
diff --git a/Mathlib/Tactic.lean b/Mathlib/Tactic.lean
index 4c45aa1547271a..b58a7798fec558 100644
--- a/Mathlib/Tactic.lean
+++ b/Mathlib/Tactic.lean
@@ -161,6 +161,7 @@ public import Mathlib.Tactic.Linter.EmptyLine
 public import Mathlib.Tactic.Linter.FindDeprecations
 public import Mathlib.Tactic.Linter.FlexibleLinter
 public import Mathlib.Tactic.Linter.GlobalAttributeIn
+public import Mathlib.Tactic.Linter.GlobalSyntax
 public import Mathlib.Tactic.Linter.HashCommandLinter
 public import Mathlib.Tactic.Linter.HaveLetLinter
 public import Mathlib.Tactic.Linter.Header
diff --git a/Mathlib/Tactic/Linter/GlobalSyntax.lean b/Mathlib/Tactic/Linter/GlobalSyntax.lean
new file mode 100644
index 00000000000000..e5c732d198d87d
--- /dev/null
+++ b/Mathlib/Tactic/Linter/GlobalSyntax.lean
@@ -0,0 +1,203 @@
+/-
+Copyright (c) 2026 Damiano Testa. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Damiano Testa
+-/
+module
+
+public meta import Lean.Elab.Import
+-- Import this linter explicitly to ensure that
+-- this file has a valid copyright header and module docstring.
+public meta import Mathlib.Tactic.Linter.Header  -- shake: keep
+import Batteries
+/-!
+#  The "globalSyntax" linter
+
+The "globalSyntax" linter emits a warning on pairs of consecuting commands with no overall effect.
+
+For instance, the linter would flag
+```lean4
+namespace X
+end X
+```
+and similarly for consecutive pairs of `open` or `section` and `end`.
+-/
+
+public meta section
+
+open Lean Elab Command Linter
+
+namespace Mathlib.Linter
+
+/--
+The `globalSyntax` linter emits a warning on pairs of consecutive commands with no overall effect.
+For instance, the linter would flag
+```lean4
+namespace X
+end X
+```
+and similarly for consecutive pairs of `open` or `section` and `end`.
+-/
+public register_option linter.globalSyntax : Bool := {
+  defValue := true
+  descr := "enable the globalSyntax linter"
+}
+/--
+`RangesToKinds` stores bookkeeping information needed by the linter.
+
+* `toKinds` maps the source `Syntax.Range` of a top-level command to its `SyntaxNodeKind`
+  preserving enough information to detect cancelling pairs.
+* `mod2` tracks the parity of coverage over the file by toggling both the start and stop
+  positions of every encountered command range; once all top-level commands have been seen,
+  this set should contain exactly the file’s import-end position and the final end-of-input.
+* `importEnd` is the position immediately after the import block (computed using `parseImports`),
+  used as one of the two distinguished positions in `mod2`.
+-/
+structure RangesToKinds where
+  /--
+  `toKinds` maps the source `Syntax.Range` of a top-level command to its `SyntaxNodeKind`
+  preserving enough information to detect cancelling pairs.
+  -/
+  toKinds : Std.HashMap Syntax.Range Name
+  /--
+  `mod2` tracks the parity of coverage over the file by toggling both the start and stop
+  positions of every encountered command range; once all top-level commands have been seen,
+  this set should contain exactly the file’s import-end position and the final end-of-input.
+  -/
+  mod2 : Std.HashSet String.Pos.Raw
+  /--
+  `importEnd` is the position immediately after the import block (computed using `parseImports`),
+  used as one of the two distinguished positions in `mod2`.
+  -/
+  importEnd : Option String.Pos.Raw
+  deriving Inhabited
+
+/--
+Toggle membership of a in the `HashSet` `h`.
+If `a ∈ h`, it is removed; otherwise it is inserted.
+-/
+def toggle {α} [BEq α] [Hashable α] (h : Std.HashSet α) (a : α) :=
+  if h.contains a then h.erase a else h.insert a
+
+/--
+Insert a `(range, kind)` pair into the `RangesToKinds` structure.
+This:
+* records that the command with kind `k` occupies `rg` in `toKinds`;
+* toggles both `rg.start` and `rg.stop` in `mod2` (so each complete range contributes
+  an even parity overall);
+* preserves the previously computed `importEnd`.
+-/
+def RangesToKinds.insert (h : RangesToKinds) (rg : Syntax.Range) (k : Name) : RangesToKinds where
+  toKinds := h.toKinds.insert rg k
+  mod2 := toggle (toggle h.mod2 rg.start) rg.stop
+  importEnd := h.importEnd
+
+/--
+Global reference used to accumulate top-level command ranges and kinds while the file is
+being elaborated. It starts empty and is progressively populated by the linter.
+-/
+initialize toKindsRef : IO.Ref RangesToKinds ← IO.mkRef {toKinds := ∅, mod2 := ∅, importEnd := none}
+
+namespace GlobalSyntax
+
+/-- A convenience pretty-printer for `Syntax.Range` used in diagnostic messages. -/
+local instance : ToString Syntax.Range where
+  toString := fun | {start, stop} => s!"({start}, {stop})"
+
+/--
+A convenience pretty-printer for `RangesToKinds` used for debugging (if needed).
+It shows all the fields of the input `RangesToKinds`.
+-/
+local instance : ToString RangesToKinds where
+  toString := fun
+  | {toKinds := toKs, mod2 := m2, importEnd := pos?} =>
+    let sorted := toKs.toArray.qsort (·.1.start < ·.1.start)
+    s!"{if let some pos := pos? then s!"{pos}" else ""}\n\
+    mod2: {m2.toArray.qsort}\n\n\
+    toKinds:\n* {"\n* ".intercalate (sorted.map (s!"{·}")).toList}"
+
+/--
+Mapping from starting command kinds to the array of ending command kinds that may close
+them at the top level. The linter uses this to recognize trivial
+"start immediately followed by end" pairs that have no global effect.
+Examples:
+* `Parser.Command.namespace` closes with `Parser.Command.end`;
+* one-line commands like `open`, `variable`, and `universe` may be followed by either
+  `end` (ending a surrounding block) or end-of-input `eoi`.
+-/
+abbrev startersEnders : NameMap (Array Name) := .ofArray (cmp := Name.quickCmp) #[
+    (``Parser.Command.namespace, #[``Parser.Command.end]),
+    (``Parser.Command.section, #[``Parser.Command.end]),
+    (``Parser.Command.open, #[``Parser.Command.end, ``Parser.Command.eoi]),
+    (``Parser.Command.variable, #[``Parser.Command.end, ``Parser.Command.eoi]),
+    (``Parser.Command.universe, #[``Parser.Command.end, ``Parser.Command.eoi]),
+  ]
+
+/--
+Compute all adjacent cancelling pairs from a sorted array of `(range, kind)` pairs.
+
+Given an array `h` of top-level commands sorted by increasing `range.start`, this returns
+every pair `(rg₁, rg₂)` such that the command of kind `h[i].2` is immediately followed by an
+"ender" kind that cancels it (according to `startersEnders`).
+
+Only adjacent pairs are considered.
+-/
+def cancellingPairs (h : Array (Syntax.Range × Name)) :
+    Array (Syntax.Range × Syntax.Range) := Id.run do
+  if this : h.size ≤ 1 then return #[] else
+  let mut pairs := #[]
+  let mut curr := h[0]
+  for i in [:h.size - 1] do
+    curr := h[i]!
+    let next := h[i + 1]!
+    if let some ender := startersEnders.get? curr.2 then
+      if ender.contains next.2 then
+        pairs := pairs.push (curr.1, next.1)
+    curr := next
+  return pairs
+
+/--
+Return the trimmed substring of `s` delimited by the `Syntax.Range` `rg`.
+This is used by the linter to echo the exact command text in diagnostic messages.
+-/
+def substringOfRange (s : String) (rg : Syntax.Range) : String :=
+  {s.toRawSubstring with startPos := rg.start, stopPos := rg.stop}.trim.toString
+
+-- Note that we explicitly avoid `withSetOptionIn`, since we want to inspect the outermost
+-- commands.
+@[inherit_doc Mathlib.Linter.linter.globalSyntax]
+def globalSyntaxLinter : Linter where run stx := do
+  unless Linter.getLinterValue linter.globalSyntax (← getLinterOptions) do
+    return
+  if (← get).messages.hasErrors then
+    return
+  if (← toKindsRef.get).toKinds.isEmpty then
+    let fm ← getFileMap
+    let (_, pos, _) ← parseImports fm.source
+    let posStx := fm.ofPosition pos
+    toKindsRef.modify (fun r => {r with toKinds := r.toKinds.insert ⟨0, posStx⟩ `Module, importEnd := some posStx})
+  if let some rg := stx.getRangeWithTrailing? then
+    -- `rg.stop == 0` should only happen when parsing `eoi`. In that case, `stx.getRange?` is
+    -- the range of width `0` at the end of the file.
+    let rg' := if rg.stop == 0 then stx.getRange?.getD default else rg
+    toKindsRef.modify (·.insert rg' stx.getKind)
+  let kindsRef ← toKindsRef.get
+  let fm ← getFileMap
+  unless kindsRef.mod2.size == 2 &&
+      (kindsRef.mod2.toArray.qsort == #[kindsRef.importEnd.getD 0, fm.positions.back!]) do
+    return
+  for (rg1, rg2) in cancellingPairs <| kindsRef.toKinds.toArray.qsort (·.1.start < ·.1.start) do
+    -- No range should have stopping position strictly before its ending position.
+    if rg1.stop < rg1.start || rg2.stop < rg2.start then
+      logWarning "This should not have happened"
+      continue
+    logLint linter.globalSyntax (.ofRange rg1)
+      m!"The command '{substringOfRange fm.source rg1}'"
+    logLint linter.globalSyntax (.ofRange rg2)
+      m!"is cancelled by '{substringOfRange fm.source rg2}'!"
+
+initialize addLinter globalSyntaxLinter
+
+end GlobalSyntax
+
+end Mathlib.Linter
diff --git a/MathlibTest/FindSyntax.lean b/MathlibTest/FindSyntax.lean
index aae407d63c9862..a945421e949109 100644
--- a/MathlibTest/FindSyntax.lean
+++ b/MathlibTest/FindSyntax.lean
@@ -3,7 +3,7 @@ import Mathlib.Tactic.FindSyntax
 infix:65 " #find_syntax_add " => Nat.add
 
 /--
-info: Found 2 uses among over 800 syntax declarations
+info: Found 2 uses among over 900 syntax declarations
 In `MathlibTest.FindSyntax`:
   «term_#find_syntax_add_»: '#find_syntax_add'
 
@@ -14,7 +14,7 @@ In `Mathlib.Tactic.FindSyntax`:
 #find_syntax "#find_syntax" approx  -- an `infix` in two files, one being the current one
 
 /--
-info: Found 1 use among over 800 syntax declarations
+info: Found 1 use among over 900 syntax declarations
 In `Init.Notation`:
   «term_∘_»: '∘'
 -/
@@ -22,7 +22,7 @@ In `Init.Notation`:
 #find_syntax "∘" approx  -- an `infixr`
 
 /--
-info: Found 1 use among over 800 syntax declarations
+info: Found 1 use among over 900 syntax declarations
 In `Init.Notation`:
   «term_∣_»: '∣'
 -/
@@ -30,7 +30,7 @@ In `Init.Notation`:
 #find_syntax "∣" approx  -- an `infix`
 
 /--
-info: Found 2 uses among over 800 syntax declarations
+info: Found 2 uses among over 900 syntax declarations
 In `Init.Notation`:
   «stx_,*»: ',*'
   «stx_,*,?»: ',*,?'
@@ -39,7 +39,7 @@ In `Init.Notation`:
 #find_syntax ",*" approx  -- generated by a `macro`
 
 /--
-info: Found 1 use among over 800 syntax declarations
+info: Found 1 use among over 900 syntax declarations
 In `Init.Notation`:
   «term~~~_»: '~~~'
 -/
@@ -47,7 +47,7 @@ In `Init.Notation`:
 #find_syntax "~~~" approx  -- a `prefix`
 
 /--
-info: Found 16 uses among over 800 syntax declarations
+info: Found 16 uses among over 900 syntax declarations
 In `Init.Tactics`:
   Lean.Parser.Tactic.mrefineMacro: 'mrefine'
   Lean.Parser.Tactic.refine: 'refine'
diff --git a/MathlibTest/Tauto.lean b/MathlibTest/Tauto.lean
index a4e570e610fa0a..2d4c26427dcecd 100644
--- a/MathlibTest/Tauto.lean
+++ b/MathlibTest/Tauto.lean
@@ -134,11 +134,9 @@ section pair_eq_pair_iff
 variable (α : Type)
 variable (x y z w : α)
 
--- This example is taken from pair_eq_pair_iff in Data.Set.Basic.
--- It currently doesn't work because `tauto` does not apply `symm`.
---example : ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧
---           (z = x ∨ z = y) ∧ (w = x ∨ w = y) → x = z ∧ y = w ∨ x = w ∧ y = z := by
---  tauto
+example : ((x = z ∨ x = w) ∧ (y = z ∨ y = w)) ∧
+           (z = x ∨ z = y) ∧ (w = x ∨ w = y) → x = z ∧ y = w ∨ x = w ∧ y = z := by
+  tauto
 
 end pair_eq_pair_iff
 
diff --git a/MathlibTest/sqrt.lean b/MathlibTest/sqrt.lean
index 78cfbfa0018ab5..1bc77c9df9d7b3 100644
--- a/MathlibTest/sqrt.lean
+++ b/MathlibTest/sqrt.lean
@@ -2,13 +2,14 @@ import Mathlib.Tactic.Eval
 import Mathlib.Tactic.NormNum.NatSqrt
 import Mathlib.Data.Rat.NatSqrt.Real
 
-open Nat
-
 /-
 Unfortunately this test run extremely slowly under `lake test`, despite on taking a few seconds
 in VSCode or under `lake build MathlibTest` or `lake env lean MathlibTest/sqrt.lean`.
 
 While we investigate, we'll turn off the test.
+
+open Nat
+
 /--
 Compute an explicit rational approximation of `√10005`, accurate to 2 million decimal places.