The set of indeterminate rings of a normal pair as a partially ordered set

Let R ì S{R\subset S} be an extension of integral domains and let R, S] be the set of intermediate rings between R and S ordered by inclusion. If (R, S) is normal pair and R, S] is finite, we do prove that there exists a semi-local Prüfer ring T with quotient field K such that R,S] @ T,K]{R,S]\cong \lbrack T,K]} (as a partially ordered set). Consequently, any problem relative to the finiteness conditions in R, S] can be investigated in the particular case where R is a semi-local Prüfer ring with quotient field S.