I assure myself that the car from the left is upholding their duty to give way and that there are no pedestrians about to enter the pedestrian crossings.

To be on the safe side, you always need to get a good overview of the traffic situation and be careful about guessing what other road users might do. You therefore need to be certain that the green car will uphold their obligation to give way.

Of course, you also need to be aware of any pedestrians about to enter the pedestrian crossing.