 Brouwer introduced choice sequences and the continuity axioms to capture the intuitionistic continuum, but these principles alone do not suffice to recover that part of traditional analysis that Brouwer considered intuitionistically sound, such as the theorem that every continuous real function on a closed interval is uniformly continuous. For this reason Brouwer proved the so-called bar theorem. It is a classically valid statement, but the proof Brouwer gave is by many considered to be no proof at all since it uses an assumption on the form of proofs for which no rigorous argument is provided. This is the reason that the bar theorem is also referred to as the bar principle. 