Hi I'm a high school student and I found this video very clear (nice diagrams and proofs). However, I found that bit at 6:53 a little unclear. I think it would be better if you added another yellow point, say z1, below or to the right of point b and show its trajectory to A(t). This way it will be easy to see that the trajectory of b will be 'bounded' by z0's and z1's trajectory to A(t) and so if b doesn't end up in A(t), it must cross at least one of the two trajectories and therefore violating 'uniqueness'