Is the == sign a congruence ? ? If yes, what is the modulus considered ? Because a congruence without modulus is meaningless.
(Funny like we all get the same idea when we lack an congruence sign on the computer )
Out of curiosity, what is the algorithm you are developing about, if not too indiscrete ?
EDIT : ah, no, I get it, this is the conditional equivalence sign in the C language. Well obviously, if , then the equality holds, because , and . I don't really get your proof (what does it show ? a proof needs words), but I think you might get somewhere if you consider dividing the right hand side with the left hand side ...