 reserve A for non empty Subset of REAL;

theorem Th4:
  for a,b,c be Real, f be Function of REAL,REAL st
    b > 0 & c > 0 holds
      ( AffineMap ( b/c,b-a*b/c) | ]. -infty,a .]
    +* AffineMap (-b/c,b+a*b/c) | [. a,+infty .[ ) | [. a-c,a+c .]
    = AffineMap ( b/c,b-a*b/c) | [. a-c,a .]
      +* AffineMap (-b/c,b+a*b/c) | [. a,a+c .]
proof
 let a,b,c be Real, f be Function of REAL,REAL;
 assume b > 0 & c > 0; then
 a-c < a & a < a+c by XREAL_1:29,XREAL_1:44;
 hence thesis by Th3;
end;
