(* Specifications: *)
Theorem auxsub : forall (H : Group U) (x : U), subgroup U H Gr -> In U (G_ U H) x -> In U G x.
Lemma eq_gt_O_dec : forall n : nat, {n = 0} + {n > 0}.
Lemma technical_lemma : forall y m : nat, S (y * m + (y + m) + m) = S y * m + (S y + m).
Lemma lt_minus2 : forall n m : nat, n < m -> 0 < m - n.
Lemma minus_n_Sm : forall n m : nat, m < n -> pred (n - m) = n - S m.
Lemma lt_succ : forall n m : nat, n <= S m -> {n <= m} + {n = S m}.