diff --git a/src/Lean/Meta/Tactic/Simp/Main.lean b/src/Lean/Meta/Tactic/Simp/Main.lean
index 67215c5976..f27329176d 100644
--- a/src/Lean/Meta/Tactic/Simp/Main.lean
+++ b/src/Lean/Meta/Tactic/Simp/Main.lean
@@ -884,8 +884,7 @@ def congrDefault (e : Expr) : SimpM Result := do
   if let some result ← tryAutoCongrTheorem? e then
     result.mkEqTrans (← visitFn result.expr)
   else
-    withParent e <| e.withApp fun f args => do
-      congrArgs (← simp f) args
+    withParent e <| simpAppUsingCongr e
 
 /-- Process the given congruence theorem hypothesis. Return true if it made "progress". -/
 def processCongrHypothesis (h : Expr) (hType : Expr) : SimpM Bool := do
diff --git a/src/Lean/Meta/Tactic/Simp/Types.lean b/src/Lean/Meta/Tactic/Simp/Types.lean
index b5da990960..c8f7ce971b 100644
--- a/src/Lean/Meta/Tactic/Simp/Types.lean
+++ b/src/Lean/Meta/Tactic/Simp/Types.lean
@@ -647,6 +647,91 @@ def congrArgs (r : Result) (args : Array Expr) : SimpM Result := do
       i := i + 1
     return r
 
+/-- Helper function for `simpAppUsingCongr` -/
+private def mkCongrFun' (e : Expr) (r : Result) (a : Expr) : MetaM Result := do
+  let e' := e.updateApp! r.expr a
+  match r.proof? with
+  | none   => return { expr := e', proof? := none }
+  | some hf =>
+    let α ← inferType a
+    let u ← getLevel α
+    let v ← getLevel (← inferType e)
+    let f := e.appFn!
+    let .forallE x _ βx _ ← whnfD (← inferType f)
+      | throwError "failed to build congruence proof, function expected{indentExpr f}"
+    let β := Lean.mkLambda x .default α βx
+    return { expr := e', proof? := mkApp6 (mkConst ``congrFun [u, v]) α β f r.expr hf a }
+
+/-- Helper function for `simpAppUsingCongr` -/
+private def mkCongrPrefix (declName : Name) (e : Expr) : MetaM Expr := do
+  let α ← inferType e.appArg!
+  let u ← getLevel α
+  let β ← inferType e
+  let v ← getLevel β
+  return mkApp2 (mkConst declName [u, v]) α β
+
+/-- Helper function for `simpAppUsingCongr` -/
+private def mkCongrArg' (e : Expr) (f : Expr) (r : Result) : MetaM Result := do
+  let e' := e.updateApp! f r.expr
+  match r.proof? with
+  | none   => return { expr := e', proof? := none }
+  | some ha =>
+    let h ← mkCongrPrefix ``congrArg e
+    return { expr := e', proof? := mkApp4 h e.appArg! r.expr f ha }
+
+/-- Helper function for `simpAppUsingCongr` -/
+private def mkCongr' (e : Expr) (r₁ r₂ : Result) : MetaM Result := do
+  let e' := e.updateApp! r₁.expr r₂.expr
+  match r₁.proof?, r₂.proof? with
+  | none,    none    => return { expr := e', proof? := none }
+  | some hf,  none    =>
+    let h ← mkCongrPrefix ``congrFun' e
+    return { expr := e', proof? := mkApp4 h e.appFn! r₁.expr hf r₂.expr }
+  | none,    some ha  =>
+    let h ← mkCongrPrefix ``congrArg e
+    return { expr := e', proof? := mkApp4 h e.appArg! r₂.expr r₁.expr ha }
+  | some hf, some ha =>
+    let h ← mkCongrPrefix ``congr e
+    return { expr := e', proof? := mkApp6 h e.appFn! r₁.expr e.appArg! r₂.expr hf ha }
+
+/--
+Given an application `e`, recursively simplifies its function and arguments and constructs a proof
+using `congrArg`, `congrFun`, `congrFun'` and `congr`.
+-/
+def simpAppUsingCongr (e : Expr) : SimpM Result := do
+  let f := e.getAppFn
+  let numArgs := e.getAppNumArgs
+  let cfg ← getConfig
+  let infos := (← getFunInfoNArgs f numArgs).paramInfo
+  let rec visit (e : Expr) (i : Nat) : SimpM Result := do
+    if i == 0 then
+      simp f
+    else
+      let i := i - 1
+      let .app f a := e | unreachable!
+      let fr ← visit f i
+      if h : i < infos.size then
+        let info := infos[i]
+        trace[Debug.Meta.Tactic.simp] "app [{i}] {infos.size} {a} hasFwdDeps: {info.hasFwdDeps}"
+        if cfg.ground && info.isInstImplicit then
+          -- We don't visit instance implicit arguments when we are reducing ground terms.
+          -- Motivation: many instance implicit arguments are ground, and it does not make sense
+          -- to reduce them if the parent term is not ground.
+          -- TODO: consider using it as the default behavior.
+          -- We have considered it at https://github.com/leanprover/lean4/pull/3151
+          mkCongrFun' e fr a
+        else if !info.hasFwdDeps then
+          mkCongr' e fr (← simp a)
+        else if (← whnfD (← inferType f)).isArrow then
+          mkCongr' e fr (← simp a)
+        else
+          mkCongrFun' e fr (← dsimp a)
+      else if (← whnfD (← inferType f)).isArrow then
+        mkCongr' e fr (← simp a)
+      else
+        mkCongrFun' e fr (← dsimp a)
+  visit e numArgs
+
 /--
 Retrieve auto-generated congruence lemma for `f`.
 
diff --git a/tests/lean/run/793.lean b/tests/lean/run/793.lean
index 9760b82d72..cacc486d27 100644
--- a/tests/lean/run/793.lean
+++ b/tests/lean/run/793.lean
@@ -10,7 +10,7 @@ foo test
 
 /--
 info: theorem test : ∀ (x : Foo✝), f✝ x = 42 :=
-fun x => of_eq_true (Eq.trans (congrArg (fun x => x = 42) (Foo.prop✝ x)) (eq_self 42))
+fun x => of_eq_true (Eq.trans (congrFun' (congrArg Eq (Foo.prop✝ x)) 42) (eq_self 42))
 -/
 #guard_msgs in
 #print test
diff --git a/tests/lean/run/ack.lean b/tests/lean/run/ack.lean
index 1490be58c1..7ed74ff009 100644
--- a/tests/lean/run/ack.lean
+++ b/tests/lean/run/ack.lean
@@ -16,10 +16,10 @@ trace: [simp] Diagnostics
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 ---
 trace: [diag] Diagnostics
-  [kernel] unfolded declarations (max: 147, num: 3):
-    [kernel] OfNat.ofNat ↦ 147
-    [kernel] Add.add ↦ 61
-    [kernel] HAdd.hAdd ↦ 61
+  [kernel] unfolded declarations (max: 176, num: 3):
+    [kernel] OfNat.ofNat ↦ 176
+    [kernel] Add.add ↦ 60
+    [kernel] HAdd.hAdd ↦ 60
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 -/
 #guard_msgs in
@@ -42,10 +42,10 @@ trace: [simp] Diagnostics
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 ---
 trace: [diag] Diagnostics
-  [kernel] unfolded declarations (max: 145, num: 3):
-    [kernel] OfNat.ofNat ↦ 145
-    [kernel] Add.add ↦ 59
-    [kernel] HAdd.hAdd ↦ 59
+  [kernel] unfolded declarations (max: 174, num: 3):
+    [kernel] OfNat.ofNat ↦ 174
+    [kernel] Add.add ↦ 58
+    [kernel] HAdd.hAdd ↦ 58
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 -/
 #guard_msgs in
@@ -68,10 +68,10 @@ trace: [simp] Diagnostics
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 ---
 trace: [diag] Diagnostics
-  [kernel] unfolded declarations (max: 145, num: 3):
-    [kernel] OfNat.ofNat ↦ 145
-    [kernel] Add.add ↦ 59
-    [kernel] HAdd.hAdd ↦ 59
+  [kernel] unfolded declarations (max: 174, num: 3):
+    [kernel] OfNat.ofNat ↦ 174
+    [kernel] Add.add ↦ 58
+    [kernel] HAdd.hAdd ↦ 58
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 -/
 #guard_msgs in
@@ -91,12 +91,12 @@ trace: [simp] Diagnostics
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 ---
 trace: [diag] Diagnostics
-  [def_eq] heuristic for solving `f a =?= f b` (max: 103, num: 1):
-    [def_eq] ack ↦ 103
-  [kernel] unfolded declarations (max: 145, num: 3):
-    [kernel] OfNat.ofNat ↦ 145
-    [kernel] Add.add ↦ 59
-    [kernel] HAdd.hAdd ↦ 59
+  [def_eq] heuristic for solving `f a =?= f b` (max: 60, num: 1):
+    [def_eq] ack ↦ 60
+  [kernel] unfolded declarations (max: 174, num: 3):
+    [kernel] OfNat.ofNat ↦ 174
+    [kernel] Add.add ↦ 58
+    [kernel] HAdd.hAdd ↦ 58
   use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
 -/
 #guard_msgs in
diff --git a/tests/lean/run/implicitRflProofs.lean b/tests/lean/run/implicitRflProofs.lean
index bdc3ee73a2..d99eabb251 100644
--- a/tests/lean/run/implicitRflProofs.lean
+++ b/tests/lean/run/implicitRflProofs.lean
@@ -9,7 +9,7 @@ theorem ex1 : f (f (x + 1)) = x + 3 := by
 info: theorem ex1 : ∀ {x : Nat}, f (f (x + 1)) = x + 3 :=
 fun {x} =>
   of_eq_true
-    (Eq.trans (congrArg (fun x_1 => x_1 = x + 3) (Eq.trans (congrArg f (f_eq x)) (f_eq (x + 1)))) (eq_self (x + 1 + 2)))
+    (Eq.trans (congrFun' (congrArg Eq (Eq.trans (congrArg f (f_eq x)) (f_eq (x + 1)))) (x + 3)) (eq_self (x + 1 + 2)))
 -/
 #guard_msgs in
 #print ex1
diff --git a/tests/lean/run/safeExp.lean b/tests/lean/run/safeExp.lean
index f17132aa03..9cac3b713a 100644
--- a/tests/lean/run/safeExp.lean
+++ b/tests/lean/run/safeExp.lean
@@ -24,8 +24,6 @@ h : k = 2008 ^ 2 + 2 ^ 2008
 ⊢ ((4032064 + 2 ^ 2008) ^ 2 + 2 ^ (4032064 + 2 ^ 2008)) % 10 = 6
 ---
 warning: declaration uses `sorry`
----
-error: (kernel) deep recursion detected
 -/
 #guard_msgs in
 example (k : Nat) (h : k = 2008^2 + 2^2008) : (k^2 + 2^k)%10 = 6 := by
diff --git a/tests/lean/run/simp5.lean b/tests/lean/run/simp5.lean
index 5d77b52d00..ebb49a87a2 100644
--- a/tests/lean/run/simp5.lean
+++ b/tests/lean/run/simp5.lean
@@ -10,7 +10,7 @@ theorem ex1 (a b c : α) : f (f a b) c = a := by
 info: theorem ex1.{u_1} : ∀ {α : Sort u_1} (a b c : α), f (f a b) c = a :=
 fun {α} a b c =>
   of_eq_true
-    (Eq.trans (congrArg (fun x => x = a) (Eq.trans (congrArg (fun x => f x c) (f_Eq a b)) (f_Eq a c))) (eq_self a))
+    (Eq.trans (congrFun' (congrArg Eq (Eq.trans (congrFun' (congrArg f (f_Eq a b)) c) (f_Eq a c))) a) (eq_self a))
 -/
 #guard_msgs in
 #print ex1
@@ -33,7 +33,7 @@ info: theorem ex2 : ∀ (p : Nat → Bool) (x : Nat), p x = true → (if p x = t
 fun p x h =>
   of_eq_true
     (Eq.trans
-      (congrArg (fun x => x = 1) (ite_cond_eq_true 1 2 (Eq.trans (congrArg (fun x => x = true) h) (eq_self true))))
+      (congrFun' (congrArg Eq (ite_cond_eq_true 1 2 (Eq.trans (congrFun' (congrArg Eq h) true) (eq_self true)))) 1)
       (eq_self 1))
 -/
 #guard_msgs in
diff --git a/tests/lean/run/simp6.lean b/tests/lean/run/simp6.lean
index 4cd447f770..39b0ab159a 100644
--- a/tests/lean/run/simp6.lean
+++ b/tests/lean/run/simp6.lean
@@ -15,7 +15,7 @@ theorem ex5 : (10 = 20) = False :=
 
 /--
 info: theorem ex5 : (10 = 20) = False :=
-of_eq_true (Eq.trans (congrArg (fun x => x = False) (eq_false_of_decide (Eq.refl false))) (eq_self False))
+of_eq_true (Eq.trans (congrFun' (congrArg Eq (eq_false_of_decide (Eq.refl false))) False) (eq_self False))
 -/
 #guard_msgs in
 #print ex5
diff --git a/tests/lean/run/simp_int_arith.lean b/tests/lean/run/simp_int_arith.lean
index f0c3d1cdb2..5231493fdd 100644
--- a/tests/lean/run/simp_int_arith.lean
+++ b/tests/lean/run/simp_int_arith.lean
@@ -286,13 +286,15 @@ info: theorem ex3 : ∀ (a b : Int), 6 ∣ a + (21 - a) + 3 * (a + 2 * b) + 12 
 fun a b =>
   of_eq_true
     (Eq.trans
-      (congrArg (fun x => x ↔ 2 ∣ a + 2 * b + 11)
-        (id
-          (norm_dvd_gcd (RArray.branch 1 (RArray.leaf b) (RArray.leaf a)) 6
-            ((((Expr.var 1).add ((Expr.num 21).sub (Expr.var 1))).add
-                  (Expr.mulL 3 ((Expr.var 1).add (Expr.mulL 2 (Expr.var 0))))).add
-              (Expr.num 12))
-            2 (Poly.add 1 1 (Poly.add 2 0 (Poly.num 11))) 3 (eagerReduce (Eq.refl true)))))
+      (congrFun'
+        (congrArg Iff
+          (id
+            (norm_dvd_gcd (RArray.branch 1 (RArray.leaf b) (RArray.leaf a)) 6
+              ((((Expr.var 1).add ((Expr.num 21).sub (Expr.var 1))).add
+                    (Expr.mulL 3 ((Expr.var 1).add (Expr.mulL 2 (Expr.var 0))))).add
+                (Expr.num 12))
+              2 (Poly.add 1 1 (Poly.add 2 0 (Poly.num 11))) 3 (eagerReduce (Eq.refl true)))))
+        (2 ∣ a + 2 * b + 11))
       (iff_self (2 ∣ a + 2 * b + 11)))
 -/
 #guard_msgs (info) in
diff --git a/tests/lean/simpZetaFalse.lean.expected.out b/tests/lean/simpZetaFalse.lean.expected.out
index 12652d3f77..029aa9d975 100644
--- a/tests/lean/simpZetaFalse.lean.expected.out
+++ b/tests/lean/simpZetaFalse.lean.expected.out
@@ -11,13 +11,15 @@ theorem ex0 : ∀ (x : Nat),
 fun x h =>
   Eq.mpr
     (id
-      (congrArg (fun x => x = 1)
-        (id
+      (congrFun'
+        (congrArg Eq
           (id
-            (have_congr' (Nat.zero_add (x * x)) fun y =>
-              ite_congr (Eq.trans (congrArg (fun x_1 => x_1 = x) h) (eq_self x)) (fun a => Eq.refl 1) fun a =>
-                Eq.refl (y + 1))))))
-    (of_eq_true (Eq.trans (congrArg (fun x => x = 1) (ite_cond_eq_true 1 (x * x + 1) (Eq.refl True))) (eq_self 1)))
+            (id
+              (have_congr' (Nat.zero_add (x * x)) fun y =>
+                ite_congr (Eq.trans (congrFun' (congrArg Eq h) x) (eq_self x)) (fun a => Eq.refl 1) fun a =>
+                  Eq.refl (y + 1)))))
+        1))
+    (of_eq_true (Eq.trans (congrFun' (congrArg Eq (ite_cond_eq_true 1 (x * x + 1) (Eq.refl True))) 1) (eq_self 1)))
 x : Nat
 h : f (f x) = x
 ⊢ (have y := x * x;
@@ -31,13 +33,15 @@ theorem ex1 : ∀ (x : Nat),
 fun x h =>
   Eq.mpr
     (id
-      (congrArg (fun x => x = 1)
-        (id
+      (congrFun'
+        (congrArg Eq
           (id
-            (have_body_congr' (x * x) fun y =>
-              ite_congr (Eq.trans (congrArg (fun x_1 => x_1 = x) h) (eq_self x)) (fun a => Eq.refl 1) fun a =>
-                Eq.refl (y + 1))))))
-    (of_eq_true (Eq.trans (congrArg (fun x => x = 1) (ite_cond_eq_true 1 (x * x + 1) (Eq.refl True))) (eq_self 1)))
+            (id
+              (have_body_congr' (x * x) fun y =>
+                ite_congr (Eq.trans (congrFun' (congrArg Eq h) x) (eq_self x)) (fun a => Eq.refl 1) fun a =>
+                  Eq.refl (y + 1)))))
+        1))
+    (of_eq_true (Eq.trans (congrFun' (congrArg Eq (ite_cond_eq_true 1 (x * x + 1) (Eq.refl True))) 1) (eq_self 1)))
 x z : Nat
 h : f (f x) = x
 h' : z = x
@@ -51,7 +55,7 @@ theorem ex2 : ∀ (x z : Nat),
         y) =
         z :=
 fun x z h h' =>
-  Eq.mpr (id (congrArg (fun x => x = z) (id (id (have_val_congr' h)))))
+  Eq.mpr (id (congrFun' (congrArg Eq (id (id (have_val_congr' h)))) z))
     (of_eq_true (Eq.trans (congrArg (Eq x) h') (eq_self x)))
 x z : Nat
 ⊢ (let α := Nat;
@@ -69,5 +73,5 @@ theorem ex4 : ∀ (p : Prop),
       fun z => p :=
 fun p h =>
   Eq.mpr
-    (id (congrArg (fun x => x = fun z => p) (id (id (have_body_congr_dep' 10 fun n => funext fun x => eq_self x)))))
+    (id (congrFun' (congrArg Eq (id (id (have_body_congr_dep' 10 fun n => funext fun x => eq_self x)))) fun z => p))
     (of_eq_true (Eq.trans (congrArg (Eq fun x => True) (funext fun z => eq_true h)) (eq_self fun x => True)))