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!] = r1*[!f1,x0,x1,x2,x3,x4!]+r2*[!
  f2,x0,x1,x2,x3,x4!]
proof
  [!(r1(#)f1+r2(#)f2),x0,x1,x2,x3,x4!] = [!(r1(#)f1),x0,x1,x2,x3,x4!] +[!(
  r2(#)f2),x0,x1,x2,x3,x4!] by Th12
    .= r1*[!f1,x0,x1,x2,x3,x4!] +[!(r2(#)f2),x0,x1,x2,x3,x4!] by Th11;
  hence thesis by Th11;
end;
