reserve r,p,x for Real;
reserve n for Element of NAT;
reserve A for non empty closed_interval Subset of REAL;
reserve Z for open Subset of REAL;

theorem
  for f1,f2,g being PartFunc of REAL,REAL, C being non empty Subset of
  REAL holds ((f1(#)f2)||C)(#)(g||C)=(f1||C)(#)((f2(#)g)||C)
proof
  let f1,f2,g be PartFunc of REAL,REAL;
  let C be non empty Subset of REAL;
  ((f1(#)f2)||C)(#)(g||C) = (f1||C)(#)(f2||C)(#)(g||C) & (f1||C)(#)((f2(#)
  g)|| C) = (f1||C)(#)((f2||C)(#)(g||C)) by INTEGRA5:4;
  hence thesis by RFUNCT_1:9;
end;
