Yeah people dramatically overestimate the difficulty of getting one's definitions correct for most problems, especially when you are doing an end to end proof rather than just axiomatizing some system. They are still worth looking at carefully, especially for AI-generated proofs where you don't get the immediate feedback that you do as a human when something you expect to be hard goes through easily, but contrary to what seems to be popular belief here they are generally much easier to verify than the corresponding proof (in the case of formally verified software, the corresponding analogy is verifying that the spec is what you want vs. verifying that the program matches the spec; the former is generally much easier).