reserve n,m for Element of NAT;
reserve h,k,r,r1,r2,x,x0,x1,x2,x3 for Real;
reserve f,f1,f2 for Function of REAL,REAL;

theorem
  cdif(f1+r(#)f2,h).(n+1).x = cdif(f1,h).(n+1).x + r* cdif(f2,h).(n+1).x
proof
  set g=r(#)f2;
  cdif(f1+r(#)f2,h).(n+1).x = cdif(f1,h).(n+1).x
       + cdif(g,h).(n+1).x by DIFF_1:22
    .= cdif(f1,h).(n+1).x + r* cdif(f2,h).(n+1).x by DIFF_1:21;
  hence thesis;
end;
