[devit]

Very unlikely that a half page proof of P!=NP is correct.

Please provide a formalization of your argument in any widely-used theorem prover (I'd recommend Lean) configured with options widely accepted to be sound.

BTW, the argument seems trivially bullshit because you say that L is in NP, and then claim that L is not P because "there exists no algorithm that...", but if L is in NP there is of course an exponential-time algorithm for L.