reserve A for non empty closed_interval Subset of REAL;

theorem
  for a,b,c,x be Real holds
    |. b*((a-x)-a)/c .| = |. b*((a+x)-a)/c .|
proof
 let a,b,c,x be Real;
 thus |. b*((a-x)-a)/c .|
  = |. (-(x*b))*(1/c) .| by XCMPLX_1:99
  .= |. -((x*b)*(1/c)) .|
  .= |. -((x*b)/c) .| by XCMPLX_1:99
  .= |. b*((a+x)-a)/c .| by COMPLEX1:52;
end;
