diff --git a/src/Lean/Meta/KAbstract.lean b/src/Lean/Meta/KAbstract.lean
index 5a2a07ec96..ee534ac938 100644
--- a/src/Lean/Meta/KAbstract.lean
+++ b/src/Lean/Meta/KAbstract.lean
@@ -34,11 +34,42 @@ def kabstract (e : Expr) (p : Expr) (occs : Occurrences := Occurrences.all) : Me
         let i ← get
         set (i+1)
         if occs.contains i then
-          pure (mkBVar offset)
+          return mkBVar offset
         else
           visitChildren ()
       else
         visitChildren ()
     visit e 0 |>.run' 1
 
+/--
+  Similar to `kabstract`, but only abstracts occurrences of `p` s.t. `pred parent? p` is true where `parent?`
+  is the parent expression for `p` if any.
+-/
+partial def kabstractWithPred (e : Expr) (p : Expr) (pred : (parent? : Option Expr) → (e : Expr) → MetaM Bool) : MetaM Expr := do
+  let e ← instantiateMVars e
+  let pHeadIdx := p.toHeadIndex
+  let pNumArgs := p.headNumArgs
+  let rec visit (parent? : Option Expr) (e : Expr) (offset : Nat) : MetaM Expr := do
+    let visitChildren : Unit → MetaM Expr := fun _ => do
+      match e with
+      | Expr.app ..          => e.withApp fun f args => return mkAppN (← visit e f offset) (← args.mapM (visit e . offset))
+      | Expr.mdata _ b _     => return e.updateMData! (← visit e b offset)
+      | Expr.proj _ _ b _    => return e.updateProj! (← visit e b offset)
+      | Expr.letE _ t v b _  => return e.updateLet! (← visit e t offset) (← visit e v offset) (← visit e b (offset+1))
+      | Expr.lam _ d b _     => return e.updateLambdaE! (← visit e d offset) (← visit e b (offset+1))
+      | Expr.forallE _ d b _ => return e.updateForallE! (← visit e d offset) (← visit e b (offset+1))
+      | e                    => return e
+    if e.hasLooseBVars then
+      visitChildren ()
+    else if e.toHeadIndex != pHeadIdx || e.headNumArgs != pNumArgs then
+      visitChildren ()
+    else if (← isDefEq e p) then
+      if (← pred parent? e) then
+        return mkBVar offset
+      else
+        visitChildren ()
+    else
+      visitChildren ()
+  visit none e 0
+
 end Lean.Meta
diff --git a/src/Lean/Meta/Tactic/Generalize.lean b/src/Lean/Meta/Tactic/Generalize.lean
index c972bc9db9..1e0ecbef09 100644
--- a/src/Lean/Meta/Tactic/Generalize.lean
+++ b/src/Lean/Meta/Tactic/Generalize.lean
@@ -16,7 +16,10 @@ structure GeneralizeArg where
   hName? : Option Name := none
   deriving Inhabited
 
-partial def generalize (mvarId : MVarId) (args : Array GeneralizeArg) : MetaM (Array FVarId × MVarId) :=
+partial def generalize
+    (mvarId : MVarId) (args : Array GeneralizeArg)
+    (pred : (parent? : Option Expr) → (e : Expr) → MetaM Bool := fun _ _ => return true)
+    : MetaM (Array FVarId × MVarId) :=
   withMVarContext mvarId do
     checkNotAssigned mvarId `generalize
     let tag ← getMVarTag mvarId
@@ -28,7 +31,7 @@ partial def generalize (mvarId : MVarId) (args : Array GeneralizeArg) : MetaM (A
         let eType ← instantiateMVars (← inferType e)
         let type ← go (i+1)
         let xName ← if let some xName := arg.xName? then pure xName else mkFreshUserName `x
-        return Lean.mkForall xName BinderInfo.default eType (← kabstract type e)
+        return Lean.mkForall xName BinderInfo.default eType (← kabstractWithPred type e pred)
       else
         return target
     let targetNew ← go 0