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;
-
-
-
-
- (λHH : ((C1 (option nat) nat (S O) (Some nat -7) -8) = (C1 (option nat) nat (S O) (Some nat -9) -8))
- eq_elim_r
- (complex (option nat) nat -8 (Some nat -7))
- (C1 (option nat) nat (S O) (Some nat -9) -8)
- (λc:(complex (option nat) nat -8 (Some nat -7)).
- (eq (option nat)
- ((λx:(complex (option nat) nat -8 (Some nat -7)).
- match x return (λy1:nat.(λy2:(option nat).(λ x:(complex (option nat) nat y1 y2).(option nat)))) with
- [ (C1 (y1:nat) (a:(option nat)) (b:nat)) => a
- | (C2 (a:(option nat)) (a1:(option nat)) (b:nat) (b1:nat) (y2:nat) (y3:(complex (option nat) nat b1 a1))) ⇒
- (Some nat -7)
- ]) c)
- (Some nat -9)))
- ?
- (C1 (option nat) nat (S O) (Some nat -7) -8)
- HH)
-
-
-
-
-destruct H;assumption.
+intros; destruct H;assumption.
qed.
theorem recursive2: ∀ x,y : nat.
C2 ? ? (None ?) ? (S O) ? O (C1 ? ? O (Some ? x) y) =
C2 ? ? (None ?) ? (S O) ? O (C1 ? ? (S O) (Some ? x) y) → False.
-intros; destruct H;
-
-
+intros; destruct H.
+qed.
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