On the fundamental conjecture of GLC, VI

The purpose of this note is to show that, a slight modification of the reasoning of our former paper [6J yields a consistency proof of a "restricted analysis" i.e. the theory of natural numbers with the following set concept: [xlA(x)}, where A(x) contains no free set variable, though it may contain bound set variables and free variables on natural numbers. This will follow immediately from the "funda- mental conjecture" on "f-closed proof-figures" which latter is to be defined below.