Not an expert but the proof is in fact entirely constructive and witnesses to the existential statement are constructible. https://math.stackexchange.com/quest

Not an expert but the proof is in fact entirely constructive and witnesses to the existential statement are constructible. https://math.stackexchange.com/questions/448527/are-the-g%C3%B6dels-incompleteness-theorems-valid-for-both-classical-and-intuitionis https://math.stackexchange.com/questions/448527/are-the-g%C3...