diff --git a/Mathlib/CategoryTheory/Sites/CoverPreserving.lean b/Mathlib/CategoryTheory/Sites/CoverPreserving.lean
index 6f29ac9836a05..88882611e28f7 100644
--- a/Mathlib/CategoryTheory/Sites/CoverPreserving.lean
+++ b/Mathlib/CategoryTheory/Sites/CoverPreserving.lean
@@ -120,7 +120,7 @@ theorem Presieve.FamilyOfElements.Compatible.functorPushforward :
 theorem CompatiblePreserving.apply_map {Y : C} {f : Y ⟶ Z} (hf : T f) :
     x.functorPushforward G (G.map f) (image_mem_functorPushforward G T hf) = x f hf := by
   unfold FamilyOfElements.functorPushforward
-  rcases e₁ : getFunctorPushforwardStructure (image_mem_functorPushforward G T hf) with
+  rcases getFunctorPushforwardStructure (image_mem_functorPushforward G T hf) with
     ⟨X, g, f', hg, eq⟩
   simpa using hG.compatible ℱ h f' (𝟙 _) hg hf (by simp [eq])
 #align category_theory.compatible_preserving.apply_map CategoryTheory.CompatiblePreserving.apply_map
diff --git a/Mathlib/MeasureTheory/Integral/SetToL1.lean b/Mathlib/MeasureTheory/Integral/SetToL1.lean
index a6468c2c05e87..dc7d4e079f130 100644
--- a/Mathlib/MeasureTheory/Integral/SetToL1.lean
+++ b/Mathlib/MeasureTheory/Integral/SetToL1.lean
@@ -638,7 +638,7 @@ theorem setToSimpleFunc_const' [Nonempty α] (T : Set α → F →L[ℝ] F') (x
 
 theorem setToSimpleFunc_const (T : Set α → F →L[ℝ] F') (hT_empty : T ∅ = 0) (x : F)
     {m : MeasurableSpace α} : SimpleFunc.setToSimpleFunc T (SimpleFunc.const α x) = T univ x := by
-  cases hα : isEmpty_or_nonempty α
+  cases isEmpty_or_nonempty α
   · have h_univ_empty : (univ : Set α) = ∅ := Subsingleton.elim _ _
     rw [h_univ_empty, hT_empty]
     simp only [setToSimpleFunc, ContinuousLinearMap.zero_apply, sum_empty,
diff --git a/Mathlib/Tactic/Cases.lean b/Mathlib/Tactic/Cases.lean
index 425ea805c77c8..5f423d3e1d625 100644
--- a/Mathlib/Tactic/Cases.lean
+++ b/Mathlib/Tactic/Cases.lean
@@ -40,7 +40,8 @@ open Lean Meta Elab Elab.Tactic
 
 open private getAltNumFields in evalCases ElimApp.evalAlts.go in
 def ElimApp.evalNames (elimInfo : ElimInfo) (alts : Array ElimApp.Alt) (withArg : Syntax)
-    (numEqs := 0) (numGeneralized := 0) (toClear : Array FVarId := #[]) :
+    (numEqs := 0) (generalized : Array FVarId := #[]) (toClear : Array FVarId := #[])
+    (toTag : Array (Ident × FVarId) := #[]) :
     TermElabM (Array MVarId) := do
   let mut names : List Syntax := withArg[1].getArgs |>.toList
   let mut subgoals := #[]
@@ -50,10 +51,15 @@ def ElimApp.evalNames (elimInfo : ElimInfo) (alts : Array ElimApp.Alt) (withArg
     names := names'
     let (fvars, g) ← g.introN numFields <| altVarNames.map (getNameOfIdent' ·[0])
     let some (g, subst) ← Cases.unifyEqs? numEqs g {} | pure ()
-    let (_, g) ← g.introNP numGeneralized
+    let (introduced, g) ← g.introNP generalized.size
+    let subst := (generalized.zip introduced).foldl (init := subst) fun subst (a, b) =>
+      subst.insert a (.fvar b)
     let g ← liftM $ toClear.foldlM (·.tryClear) g
-    for fvar in fvars, stx in altVarNames do
-      g.withContext <| (subst.apply <| .fvar fvar).addLocalVarInfoForBinderIdent ⟨stx⟩
+    g.withContext do
+      for (stx, fvar) in toTag do
+        Term.addLocalVarInfo stx (subst.get fvar)
+      for fvar in fvars, stx in altVarNames do
+        (subst.get fvar).addLocalVarInfoForBinderIdent ⟨stx⟩
     subgoals := subgoals.push g
   pure subgoals
 
@@ -62,7 +68,7 @@ elab (name := induction') "induction' " tgts:(Parser.Tactic.casesTarget,+)
     usingArg:((" using " ident)?)
     withArg:((" with" (ppSpace colGt binderIdent)+)?)
     genArg:((" generalizing" (ppSpace colGt ident)+)?) : tactic => do
-  let targets ← elabCasesTargets tgts.1.getSepArgs
+  let (targets, toTag) ← elabCasesTargets tgts.1.getSepArgs
   let g :: gs ← getUnsolvedGoals | throwNoGoalsToBeSolved
   g.withContext do
     let elimInfo ← getElimNameInfo usingArg targets (induction := true)
@@ -88,12 +94,12 @@ elab (name := induction') "induction' " tgts:(Parser.Tactic.casesTarget,+)
         ElimApp.setMotiveArg g elimArgs[elimInfo.motivePos]!.mvarId! targetFVarIds
         g.assign result.elimApp
         let subgoals ← ElimApp.evalNames elimInfo result.alts withArg
-          (numGeneralized := fvarIds.size) (toClear := targetFVarIds)
+          (generalized := fvarIds) (toClear := targetFVarIds) (toTag := toTag)
         setGoals <| (subgoals ++ result.others).toList ++ gs
 
 elab (name := cases') "cases' " tgts:(Parser.Tactic.casesTarget,+) usingArg:((" using " ident)?)
   withArg:((" with" (ppSpace colGt binderIdent)+)?) : tactic => do
-  let targets ← elabCasesTargets tgts.1.getSepArgs
+  let (targets, toTag) ← elabCasesTargets tgts.1.getSepArgs
   let g :: gs ← getUnsolvedGoals | throwNoGoalsToBeSolved
   g.withContext do
     let elimInfo ← getElimNameInfo usingArg targets (induction := false)
@@ -108,5 +114,5 @@ elab (name := cases') "cases' " tgts:(Parser.Tactic.casesTarget,+) usingArg:(("
       ElimApp.setMotiveArg g motive.mvarId! targetsNew
       g.assign result.elimApp
       let subgoals ← ElimApp.evalNames elimInfo result.alts withArg
-         (numEqs := targets.size) (toClear := targetsNew)
+         (numEqs := targets.size) (toClear := targetsNew) (toTag := toTag)
       setGoals <| subgoals.toList ++ gs
diff --git a/lake-manifest.json b/lake-manifest.json
index 13c561aed7980..fe2644d28f3e5 100644
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -4,10 +4,10 @@
  [{"url": "https://github.com/leanprover/std4",
    "type": "git",
    "subDir": null,
-   "rev": "0f6bc5b32bf5b0498902d3b5f0806c75530539d5",
+   "rev": "4f632e6fac86f6c3b7d4ac127c0ce8b06ab86f63",
    "name": "std",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
+   "inputRev": "4f632e6fac86f6c3b7d4ac127c0ce8b06ab86f63",
    "inherited": false,
    "configFile": "lakefile.lean"},
   {"url": "https://github.com/leanprover-community/quote4",
diff --git a/lakefile.lean b/lakefile.lean
index db2b89928d405..2cde560b467f8 100644
--- a/lakefile.lean
+++ b/lakefile.lean
@@ -26,7 +26,7 @@ package mathlib where
 meta if get_config? doc = some "on" then -- do not download and build doc-gen4 by default
 require «doc-gen4» from git "https://github.com/leanprover/doc-gen4" @ "main"
 
-require std from git "https://github.com/leanprover/std4" @ "main"
+require std from git "https://github.com/leanprover/std4" @ "4f632e6fac86f6c3b7d4ac127c0ce8b06ab86f63"
 require Qq from git "https://github.com/leanprover-community/quote4" @ "master"
 require aesop from git "https://github.com/leanprover-community/aesop" @ "master"
 require proofwidgets from git "https://github.com/leanprover-community/ProofWidgets4" @ "v0.0.25"
diff --git a/lean-toolchain b/lean-toolchain
index 3f21e50bd46eb..0a830983958ad 100644
--- a/lean-toolchain
+++ b/lean-toolchain
@@ -1 +1 @@
-leanprover/lean4:v4.5.0-rc1
+leanprover/lean4:nightly-2023-12-22