P and NP

Hello, /prog/.
I'm not sure if it goes here, so sorry if it doesn't.

This is a doubt i came up while studying about complexity classes.
How can one prove formally that P is contained in NP?
I can see the obviousity  of this sentence, but i can't offer a formal answer. Every paper i read about that just skips this part and uses this fact as granted.

Thanks.

The definition of a non-deterministic Turing machine includes the one of a deterministic. So every program that runs in O(n^k) on a deterministic machine, works a non-deterministic one. They just don't use this retarded ``non-deterministic choice'' operation the NTM implements.

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