As noted, most of the time (including in this dictionary definition), we do not distinguish between "proven false" and "not proven true", because there are very

As noted, most of the time (including in this dictionary definition), we do not distinguish between "proven false" and "not proven true", because there are very few cases where such a distinction matters. "Belief"s are not immutable - we believe in things, but given evidence we can change those beliefs. If I say "I believe in man-made climate change", I am not arguing that I would not change my opinion if evidence was provided that it wasn't the case.