theorem Th55:
  for a,b being Real st a <> 0 holds rng AffineMap(a,b) = REAL
proof
  let a,b be Real such that
A1: a <> 0;
  thus rng AffineMap(a,b) c= REAL;
  let e be object;
  assume e in REAL;
  then reconsider r = e as Element of REAL;
  reconsider s = (r - b)/a as Element of REAL by XREAL_0:def 1;
  AffineMap(a,b).s = a*s + b by Def4
    .= r - b + b by A1,XCMPLX_1:87
    .= r;
   then r in rng AffineMap(a,b) by FUNCT_2:4;
  hence thesis;
end;
