proposition: Lemma trunc : forall {A} {n} (p:nat), n > p -> t A n -> t A (n - p).
proof: Proof. intros A n p; induction p as [| p f]; intros H v. - rewrite Nat.sub_0_r. exact v. - apply shiftout. rewrite <- Nat.sub_succ_l. + exact (f (Nat.lt_le_incl _ _ H) v). + exact (Nat.lt_le_incl _ _ H). Defined.
imports: Arith_base