theorem Th42:
  for S being IC-Ins-separated non empty
  with_non-empty_values Mem-Struct over N,
      p being PartState of S
  holds dom Initialize p = dom p \/ {IC S}
proof let S be IC-Ins-separated non empty
   with_non-empty_values Mem-Struct over N;
  let p being PartState of S;
  thus dom Initialize p
     = dom p \/ dom Start-At(0,S) by FUNCT_4:def 1
    .= dom p \/ {IC S};
end;
