Section GroupProperties.
Context `{G : Group}.
induction n; intuition; simpl in *.
rewrite IHn.
apply left_identity.
Qed.
induction n1; intuition; simpl in *.
rewrite left_identity.
trivial.
rewrite IHn1.
rewrite associativity.
trivial.
Qed.

Theorem groupExp_mult : forall n2 n1 x,
((x^n1)^n2) = (x^(n1 * n2)).