Botvinnik is not interested at all in the a-file. The plan is Nc4-Nd6, with a very active position.
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Boris Spassky Mark Taimanov URS-ch 1956 Black to move
This is a typical position in the Ruy López. Black has managed to get the pawn to d4 and now makes a standard maneuver to gain control of the central dark squares.
With this sequence, Black eliminates the security guards of the d4-square and leaves White with a structure more typical of a Sicilian Defense, with a backward pawn on d3. The d4-square can be occupied by a black minor piece. The position is still balanced because Black has also compromised his structure on the queenside.
Developing a piece and avoiding the capture on e5, while at the same time planning to eliminate a defender of the d4-square.
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Petar Trifunovic Vasja Pirc Interzonal 1948 Black to move
This position comes from a Queen's gambit, Carlsbard structure. Black has played a6 to momentarily stop the minority attack with b5, and has traded the dark-squared bishops with the g6-Nh5 manoeuvre. To complete the opening success, it is important to trade a key piece for the white attack. How to continue?
Great move. Black simply opens the diagonal for the bishop, which is our worst piece by far in this position and we intend to trade it for the d3-bishop, which is a good one. Once we have eliminated the d3-bishop, c4 becomes a weak square that we can use!
The idea we mentioned. We eliminate the light-squared bishop, key piece to control e4-c4 and that supports the b5-push.
Otherwise Black plays ...c5 and frees his light-squared bishop. This is the only plan that fights for an advantage. The c5-square cannot be controlled by black pawns and therefore is a nice outpost for a white minor piece.
15.Bc5 seems natural but is strongly met with Nf4! winning a tempo over the queen. After 16.Qf3 then Black is fine after a5! intending a4 and Bc8.