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You're mixing up programming with computer science. The former is a task that does not necessarily need any math (e.g. web development), the latter is literally math (e.g. category algebra).

Edit: clarification

It doesn't come up because it is too abstract. About the only languages I can think of that will accept existential statements are theorem provers. My favourite is Isabelle/HOL.

In fact, the notation used by the lecturer is sloppy. Numbers 1..N is not a rigorous domain definition. (Unknown if real or natural.)

I'm not sure I buy your claim that mathematical notation is "close to the metal".