i am confused in this position

i have seen that if black has timeout here a win is given to white like positions similar to this . Even I have won a position like this once with time but i dont think there is a way for white to checkmate black
lichess.org/analysis/8/8/8/7k/6p1/8/3BK3/8_w_-_-_0_1

@tijilsingh white can promote pawn to queen and win the game

how black can promote and win my question is how can white mate it isnt possible and white has one bishop and black has a pawn @fish224 and the pawn cant promote into white bishop so it isnt possible according to me

White can mate. It's possible

1. Bc3 Kb5 2. Kb3 a4+ 3. Kc2 a3 4. Bd2 Kc4 5. Kd1 Kb3 6. Ke1 Ka2 7. Kd1 Ka1 8. Kc1 a2 9. Bc3#

lichess.org/analysis/8/8/8/8/8/2B5/p7/k1K5_b_-_-_0_1 we get this position at the end

what about this then @fish224 lichess.org/analysis/8/8/8/7k/6p1/8/3BK3/8_w_-_-_0_1

black can promote into a knight and mate is possible if black helps you to mate him.

In this position white can checkmate black too, because black can promote to a knight

@MrWoodman123 i mean for white