Two Bishops Checkmate

First, we can move the light-squared bishop up to make the wall smaller.

The enemy king can't move sideways, so he has to move towards the edge of the board.

Then, we can move our other bishop next to our first one.

This the same wall as before, but now we're one step closer to the edge!

We also have to move our king closer so that our bishops can move the wall.

Without our king's protection, the enemy king can capture our bishop if it gets too close!

Notice that this is the same position we started with, but a square higher!

Now, make the wall smaller with the dark-squared bishop.

But what happens if the enemy king moves diagonally this way?

If we try the same thing now, we've left a hole in the wall! The king can escape!

So how can we make the wall smaller?

We can mix up the order a little by moving our king up first.

Because our king covers the hole in the wall, the enemy king has to move in the other direction.

Now we can move our bishop next to the other one, forming the whole wall again.

We have to get the bishop on the left to the red square to move the wall.

But, you still have to cover the e7 square so the enemy king doesn't attack our light-squared bishop.

So, we can move it back...

...and move our king to where the bishop was!

Now, our king covers the e7 square, so our dark-squared bishop can go to f6!

And no matter where the enemy king moves again, move the bishop next to the other one.

Notice this is the same position as the starting position!

Now, just follow the same pattern to force the king to the corner.

Repeat the steps from before until our king moves two squares from the edge (3 including the king).

Now, we can complete our checkmate pattern.

First, make sure the king can't move back to the center of the board.

Cut off the king's escape with the dark-squared bishop.

Now, the enemy king is stuck moving between g8 and h8.

This lets us shift our pieces around to create the checkmate.

Move the light-squared bishop back.

Then, move the king to the square the bishop was on.

The king now covers h7, so we can move our light-squared bishop off the diagonal.

Move the light-squared bishop around to force the king into the corner.

Can you see what's coming next?

Moving the dark-squared bishop to e5 is checkmate!