Say a student is completing a problem set and is asked to prove P. If the student writes "P therefore Q therefore True since Q was proven in class. QED" then th

Say a student is completing a problem set and is asked to prove P. If the student writes "P therefore Q therefore True since Q was proven in class. QED" then the student has committed a significant error in reasoning. If the student instead just writes "P. Q. True. QED" then they are writing the above in a more terse manner and have equally committed an error in their reasoning. If they first write that but then amend in some "iff"s between each step I'll give them full credit (assuming iffs are valid) but be slightly worried that they just learned that you need to put an "iff" in those spots to keep the teacher happy but don't understand why. If a strategy is not guaranteed to give proof, then you need to verify afterwards that the putative proof is in fact a proof. Just as if you get a potential solution to an equation (via solving a more general equation, perhaps), you have not "solved" the original equation until you actually check that solution, even if your putative solution is the true one. If a student does not do the "check if steps are reversible" part, then they have not written a proof even if every step is reversible! That's what's lacking form their proof.