This result formalizes let , let B n+1 :=\ =( ', n+1 ) C n C:| |<1\ , and let the Siegel upper half-space be U n:=\ (z',w) C n C: w>|z'| 2\ . It supports the chapter's treatment of CR geometry, [boundary regularity](/theorems/99), and holomorphic extension in several complex variables.