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    $\begingroup$ Can you explain better the problem? If you want to prove 0+d=d by induction (that is a very good idea), the two cases should be 0+0=0 and 0 + succ d = succ d knowing that 0 + d = d. $\endgroup$
    – Ricky
    Commented Jan 19 at 15:54
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    $\begingroup$ Ah, I see, you are trying to prove even the induction step by induction. Well, this is not a very good idea. But notice that you now have a new assumption! $\endgroup$
    – Ricky
    Commented Jan 19 at 16:01
  • $\begingroup$ Just use induction once :-) $\endgroup$
    – Kevin Buzzard
    Commented Jan 19 at 16:23