if the pc7 was not there, we could have the following mate :
1. Dg3+ Re2 2. Txe7+ ROxe7# (note that the path of ROa7 is unique thanks to pc6)
due to the disappearance of the c7-pawn, ROa8 controls c3 by c7 and d5 .
So you have to arrive in the position of the statement without the c7-pawn. It just needs 17 moves !
1.e5+♔f1 2.f7+♔e1 3.♗d2+♔f1 4.♗f4♔e1
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