reserve h,r,r1,r2,x0,x1,x2,x3,x4,x5,x,a,b,c,k for Real,
  f,f1,f2 for Function of REAL,REAL;

theorem
  [!(r1(#)f1+r2(#)f2),x0,x1,x2,x3,x4,x5!] = r1*[!f1,x0,x1,x2,x3,x4,x5!]+
  r2*[!f2,x0,x1,x2,x3,x4,x5!]
proof
  [!(r1(#)f1+r2(#)f2),x0,x1,x2,x3,x4,x5!] = [!(r1(#)f1),x0,x1,x2,x3,x4,x5
  !] +[!(r2(#)f2),x0,x1,x2,x3,x4,x5!] by Th15
    .= r1*[!f1,x0,x1,x2,x3,x4,x5!] +[!(r2(#)f2),x0,x1,x2,x3,x4,x5!] by Th14;
  hence thesis by Th14;
end;
