Disclaimer: I am a software engineer with a Bsc. in Informatics, and no signifcant background in Mathematics (sadly).
I have a real life programming problem, which is equivalent to finding all prime implicants of a given boolean expression which does not contain negations, and then picking the 'best' one.
My main issue is that I need to keep track of metadata to decide on the 'best' prime implicant based on not-yet-defined metrics. This metadata is not defined for negations, which is why I'd avoid them if possible.
Assume that I can trivially transform my boolean expression into a DNF by repeatedly utilizing associativity (?) to remove all braces. My education is enough for that task. I can then remove all duplicate terms by applying ABB = AB and A+B+B = A+B.
Is this negation-free DNF without duplicates a disjunction of prime implicants?
I cannot think of any cases that would contradict this assumption. However, I'm really rusty in terms of formal proofs and do not trust myself enough to assume that my proof would be correct. Thank you for your time and assistance.