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Why Progress is guaranteed in test and set lock(TSL) because if we look at spin lock problem in which let’s say P1 having lower priority is in critical section and when P2 having higher priority comes which is interested in entering into Critical Section then it stops P2 from entering then how can we say that progress is guaranteed in test and set lock?
in Operating System
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When we talk about  guaranteed Progress, we see that because of an process other process is not hauled.

for example we have process P1 and p2

We see that if process p1 don”t want to enter the critical state than this should not stop the process P1 to enter

When we talk about spin lock the situation is very different

Because P1 is inside the critical section and it is forcefully stopped but it is still inside the critical section because of no CPU, process P1 is stuck inside the critical section so because of this P2 is not getting the critical section.

Here process are are interfering the entrance, it is because of OS because it is not giving the chance to P1 to come out of critical section.
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