intros a0 b0 c0 H'0 H'1 H'2 H'3.
apply H'2; auto.
rewrite H'3; auto.
intros a0 b0 c0 H'0 H'1 H'2 H'3.
replace a0 with (a0 - b0); auto.
rewrite H'3; auto with arith.
Qed.

Theorem gcd_inv_Or : forall a b : nat, gcd_spec a 0 b -> a = b.
intros a b H'.