diff --git a/src/Lean/Meta/Tactic/Grind/Injective.lean b/src/Lean/Meta/Tactic/Grind/Injective.lean
index 248cfa7737..156bf63736 100644
--- a/src/Lean/Meta/Tactic/Grind/Injective.lean
+++ b/src/Lean/Meta/Tactic/Grind/Injective.lean
@@ -5,7 +5,8 @@ Authors: Leonardo de Moura
 -/
 module
 prelude
-public import Lean.Meta.Tactic.Grind.Theorems
+public import Lean.Meta.Tactic.Grind.EMatchTheorem
+import Lean.Meta.FunInfo
 public section
 namespace Lean.Meta.Grind
 
@@ -37,16 +38,33 @@ private builtin_initialize injectiveTheoremsExt : SimpleScopedEnvExtension Injec
       initial  := {}
     }
 
-private def getSymbols (proof : Expr) : MetaM (List HeadIndex) := do
+private partial def getSymbols (proof : Expr) : MetaM (List HeadIndex) := do
   let type ← inferType proof
   forallTelescope type fun _ type => do
     unless type.isAppOfArity ``Function.Injective 3 do
       throwError "invalid `[grind inj]` theorem, resulting type is not of the form `Function.Injective <fun>`{indentExpr type}"
-    let f := type.appArg!
-    let cs : NameSet := f.foldConsts (init := {}) fun declName s => s.insert declName
+    let f := type.appArg!.eta
+    let cs ← collectFnNames f
     if cs.isEmpty then
-      throwError "invalid `[grind inj]` theorem, injective function must use at least one constant symbol{indentExpr f}"
+      throwError "invalid `[grind inj]` theorem, injective function must use at least one constant function symbol{indentExpr f}"
     return cs.toList.map (.const ·)
+where
+  collectFnNames (f : Expr) : MetaM NameSet := do
+    if let .const declName _ := f then
+      return { declName }
+    else
+      Prod.snd <$> (go f |>.run {})
+
+  go (e : Expr) : StateRefT NameSet MetaM Unit := do
+    if e.isApp then e.withApp fun f args => do
+      if let .const declName _ := f then
+        modify (·.insert declName)
+      let kinds ← NormalizePattern.getPatternArgKinds f args.size
+      for h : i in *...args.size do
+        let arg  := args[i]
+        let kind := kinds[i]?.getD .relevant
+        if kind matches .relevant | .typeFormer then
+          go arg
 
 private def symbolsToNames (s : List HeadIndex) : List Name :=
   s.map fun
diff --git a/tests/lean/run/grind_inj.lean b/tests/lean/run/grind_inj.lean
index 4d2fd4c235..2516da8e72 100644
--- a/tests/lean/run/grind_inj.lean
+++ b/tests/lean/run/grind_inj.lean
@@ -45,3 +45,22 @@ error: invalid `[grind inj]` theorem, resulting type is not of the form `Functio
 #guard_msgs in
 @[grind inj] theorem succ_inj' : succ x = succ y → x = y := by
   grind [succ]
+
+/-- trace: [grind.inj] mul_2_inj: [HMul.hMul, OfNat.ofNat] -/
+#guard_msgs in
+set_option trace.grind.inj true in
+@[grind inj] theorem mul_2_inj : Function.Injective (2 * ·) := by
+  grind [Function.Injective]
+
+def Array.IsId (as : Array Nat) : Prop :=
+  ∀ i : Fin as.size, as[i] = i
+
+/-- trace: [grind.inj] array_inj: [Array, GetElem?.getElem?, Fin, Array.size] -/
+#guard_msgs in
+set_option trace.grind.inj true in
+@[grind inj] theorem array_inj {as : Array Nat} (h : as.IsId) : Function.Injective (as[·]? : Fin as.size → Option Nat) := by
+  intro a b; simp
+  have ha := h a
+  have hb := h b
+  simp at ha hb
+  grind