Prove that a code is d-error-correcting if and only if it is (2d)-error detecting.

The Fano code is 2 error-detecting, and it is 1-error-correcting, so i was thinking of using this as the basis step of induction..

assume: d error correcting $\displaystyle \implies$ 2d error detecting

prove: d+1 error correcting $\displaystyle \implies$ 2(d+1) error detecting

d + 1 error correcting $\displaystyle \implies$ 2d error detecting + 2 error detecting.(induction assumption)

= 2(d+1)-error detecting.

if this works then.... i can just use the same method to

Prove: that 2d error detecting $\displaystyle \implies$ d error correcting