--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "logic/equality.ma".
+include "nat/nat.ma".
+
+universe constraint Type[0] < Type[1].
+universe constraint Type[1] < Type[2].
+universe constraint CProp[0] < CProp[1].
+universe constraint CProp[1] < CProp[2].
+universe constraint Type[0] ≤ CProp[0].
+universe constraint CProp[0] ≤ Type[0].
+universe constraint Type[1] ≤ CProp[1].
+universe constraint CProp[1] ≤ Type[1].
+universe constraint Type[2] ≤ CProp[2].
+universe constraint CProp[2] ≤ Type[2].
+
+ninductive A : Type[0] ≝
+ | K : nat → A
+ | W : nat → A.
+
+nlet rec A_rect (Q_:∀x_3:A.Type[0]) H_K H_W x_3 on x_3 :Q_ x_3≝
+match x_3 with [K x_4⇒H_K x_4|W x_5⇒H_W x_5].
+
+nlemma yy : ∀x,y. K x = W y → False.
+#x; #y; #H;
+nchange with
+ (match K x return λ_.Prop with [ K _ ⇒ False | W _ ⇒ True]);
+nrewrite > H; nwhd; napply I;
+nqed.
+
+nlemma xx : ∀x,y. K x = K y → x = y.
+# x; #y; #H;
+nchange with
+ (match K x return λ_.Prop with [ K a ⇒ a = y | W b ⇒ b = y]);
+nrewrite > H; nwhd; napply (refl_eq ??);
+nqed.
+
+naxiom P : Prop.
+
+nlemma ww : ∀a,b:A. a = b → P.
+#a; #b;
+ncases a; ncases b;
+#x; #y; #H;
+##[
+
+##| nelim (yy ?? H);
+##| nelim (yy ?? H);
+
+##]
+
+
+
+
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