(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/tests/discriminate".
+
include "logic/equality.ma".
include "nat/nat.ma".
| C1 : ∀x:nat.∀a:A.∀b:B. complex A B b a
| C2 : ∀a,a1:A.∀b,b1:B.∀x:nat. complex A B b1 a1 → complex A B b a.
-
theorem recursive1: ∀ x,y : nat.
(C1 ? ? O (Some ? x) y) =
(C1 ? ? (S O) (Some ? x) y) → False.
-intros; destruct H;
+intros; destruct H.
qed.
theorem recursive2: ∀ x,y,z,t : nat.
(C1 ? ? t (Some ? x) y) =
(C1 ? ? z (Some ? x) y) → t=z.
-intros; destruct H;assumption.
+intros; destruct H; reflexivity.
qed.
theorem recursive3: ∀ x,y,z,t : nat.
C2 ? ? (None ?) ? (S O) ? z (C1 ? ? (S O) (Some ? x) y) =
C2 ? ? (None ?) ? (S O) ? t (C1 ? ? (S O) (Some ? x) y) → z=t.
-intros; destruct H;assumption.
+intros; destruct H; reflexivity.
qed.
theorem recursive4: ∀ x,y,z,t : nat.
C2 ? ? (None ?) ? (S O) ? z (C1 ? ? (S O) (Some ? z) y) =
C2 ? ? (None ?) ? (S O) ? t (C1 ? ? (S O) (Some ? x) y) → z=t.
-intros; destruct H;assumption.
+intros; destruct H; reflexivity.
qed.
theorem recursive2: ∀ x,y : nat.