diff --git a/src/Lean/Meta/Injective.lean b/src/Lean/Meta/Injective.lean
index d4d5cef40826..c9fb53a20e19 100644
--- a/src/Lean/Meta/Injective.lean
+++ b/src/Lean/Meta/Injective.lean
@@ -30,6 +30,14 @@ def elimOptParam (type : Expr) : CoreM Expr := do
     else
       return .continue
 
+def occursOrInType (e : Expr) (t : Expr) : MetaM Bool := do
+  let_fun f (s : Expr) := do
+    if !s.isFVar then
+      return s == e
+    let ty ← inferType s
+    return s == e || e.occurs ty
+  return (← t.findM? f).isSome
+
 private partial def mkInjectiveTheoremTypeCore? (ctorVal : ConstructorVal) (useEq : Bool) : MetaM (Option Expr) := do
   let us := ctorVal.levelParams.map mkLevelParam
   let type ← elimOptParam ctorVal.type
@@ -57,7 +65,7 @@ private partial def mkInjectiveTheoremTypeCore? (ctorVal : ConstructorVal) (useE
         match (← whnf type) with
         | Expr.forallE n d b _ =>
           let arg1 := args1.get ⟨i, h⟩
-          if arg1.occurs resultType then
+          if ← occursOrInType arg1 resultType then
             mkArgs2 (i + 1) (b.instantiate1 arg1) (args2.push arg1) args2New
           else
             withLocalDecl n (if useEq then BinderInfo.default else BinderInfo.implicit) d fun arg2 =>
@@ -103,6 +111,7 @@ private def mkInjectiveTheorem (ctorVal : ConstructorVal) : MetaM Unit := do
     | return ()
   let value ← mkInjectiveTheoremValue ctorVal.name type
   let name := mkInjectiveTheoremNameFor ctorVal.name
+  trace[Meta.injective] "theorem {name} : {type} := {value}"
   addDecl <| Declaration.thmDecl {
     name
     levelParams := ctorVal.levelParams
@@ -134,6 +143,7 @@ private def mkInjectiveEqTheorem (ctorVal : ConstructorVal) : MetaM Unit := do
     | return ()
   let value ← mkInjectiveEqTheoremValue ctorVal.name type
   let name := mkInjectiveEqTheoremNameFor ctorVal.name
+  trace[Meta.injective] "theorem {name} : {type} := {value}"
   addDecl <| Declaration.thmDecl {
     name
     levelParams := ctorVal.levelParams
diff --git a/src/Lean/Util/FindExpr.lean b/src/Lean/Util/FindExpr.lean
index 56217625b889..f37fbbe00259 100644
--- a/src/Lean/Util/FindExpr.lean
+++ b/src/Lean/Util/FindExpr.lean
@@ -55,6 +55,18 @@ def find? (p : Expr → Bool) (e : Expr) : Option Expr :=
 def occurs (e : Expr) (t : Expr) : Bool :=
   (t.find? fun s => s == e).isSome
 
+def findM? [Monad m] (p : Expr → m Bool) (e : Expr) : m (Option Expr) := do
+  if ← p e then
+    return some e
+  else match e with
+    | .forallE _ d b _ => findM? p d <||> findM? p b
+    | .lam _ d b _     => findM? p d <||> findM? p b
+    | .mdata _ b       => findM? p b
+    | .letE _ t v b _  => findM? p t <||> findM? p v <||> findM? p b
+    | .app f a         => findM? p f <||> findM? p a
+    | .proj _ _ b      => findM? p b
+    | _                => pure none
+
 /--
   Return type for `findExt?` function argument.
 -/
diff --git a/tests/lean/run/3386.lean b/tests/lean/run/3386.lean
new file mode 100644
index 000000000000..f470fdb72993
--- /dev/null
+++ b/tests/lean/run/3386.lean
@@ -0,0 +1,9 @@
+/- Verify that injectivity lemmas are constructed with the right level of generality
+   in order to avoid type errors.
+-/
+
+inductive Tyₛ : Type (u+1)
+| SPi : (T : Type u) -> (T -> Tyₛ) -> Tyₛ
+
+inductive Tmₛ.{u} :  Tyₛ.{u} -> Type (u+1)
+| app : Tmₛ (.SPi T A) -> (arg : T) -> Tmₛ (A arg)