+rewrite < H in \vdash (? ? ? ((\lambda j.((\lambda w.%) ?)) ?)).
+
+rewrite < H in \vdash (? ? % ?).
+
+simplify in \vdash (? ? ? ((\lambda _.((\lambda _.%) ?)) ?)).
+
+rewrite < H in \vdash (? ? ? (% ?)).
+simplify.
+reflexivity.
+qed.
+
+theorem t: \forall n. 0=0 \to n = n + 0.
+ intros.
+ apply plus_n_O.
+qed.
+
+(* In this test "rewrite < t" should open a new goal 0=0 and put it in *)
+(* the goallist so that the THEN tactical closes it using reflexivity. *)
+theorem foo: \forall n. n = n + 0.
+ intros.
+ rewrite < t; reflexivity.
+qed.
+
+theorem test_rewrite_in_hyp:
+ \forall n,m. n + 0 = m \to m = n + 0 \to n=m \land m+0=n+0.
+ intros.
+ rewrite < plus_n_O in H.
+ rewrite > plus_n_O in H1.
+ split; [ exact H | exact H1].
+qed.
+
+theorem test_rewrite_in_hyp2:
+ \forall n,m. n + 0 = m \to n + 0 = m \to n=m \land n+0=m.
+ intros.
+ rewrite < plus_n_O in H H1 \vdash (? ? %).
+ split; [ exact H | exact H1].
+qed.