 It follows that POS is derivable in INT, in which the full fan theorem, not just FT\(_D\), is a standard principle. The situation is quiet the opposite in RUSS, where there exist both a detachable bar of \(2^*\) that is not uniform and a positive-valued, uniformly continuous function on \([0,1]\) that has infimum equal to 0; see Chapters 5 and 6 of Bridges &amp; Richman [1987]. 