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+
+Lemma test1 : 
+forall (v : nat) (f g : nat -> nat),
+f v = g v.
+intros. f_equal.
+(* 
+Goal in v8.5: f v = g v
+Goal in v8.4: v = v -> f v = g v
+Expected: f = g
+*)
+Admitted.
+
+Lemma test2 : 
+forall (v u : nat) (f g : nat -> nat),
+f v = g u.
+intros. f_equal.
+(* 
+In both v8.4 And v8.5
+Goal 1: v = u -> f v = g u
+Goal 2: v = u
+
+Expected Goal 1: f = g
+Expected Goal 2: v = u
+*)
+Admitted.
+
+Lemma test3 : 
+forall (v : nat) (u : list nat) (f : nat -> nat) (g : list nat -> nat),
+f v = g u.
+intros. f_equal.
+(* 
+In both v8.4 And v8.5, the goal is unchanged.
+*)
+Admitted.
+
+Require Import List.
+Lemma foo n (l k : list nat) : k ++ skipn n l = skipn n l.
+Proof. f_equal.
+(*
+  8.4: leaves the goal unchanged, i.e. k ++ skipn n l = skipn n l
+  8.5: 2 goals, skipn n l = l -> k ++ skipn n l = skipn n l
+    and skipn n l = l
+*)
+Require Import List.
+Fixpoint replicate {A} (n : nat) (x : A) : list A :=
+  match n with 0 => nil | S n => x :: replicate n x end.
+Lemma bar {A} n m (x : A) : 
+  skipn n (replicate m x) = replicate (m - n) x ->
+  skipn n (replicate m x) = replicate (m - n) x.
+Proof. intros. f_equal.
+(* 8.5: one goal, n = m - n *)