Hello.
Let's imagine I report a shop robbery to the police or just describe to my friend what I saw yesterday:
A/the shop assistant raised the alarm when he saw a gun in a/the man's pocket.
Is it correct to use the indefinite article before 'shop' and 'man' as it is first mention?
Yes correct
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A/the shop assistant raised the alarm when he saw a gun in the man's pocket.
Here we have a specific incident, and by implication, a particular suspect. I would use the definite article before "man." Compare with this sentence where the situation is hypothetical.
Shop assistants should raise an alarm if they see a gun in a man's pocket.