reserve i for Integer,
  a, b, r, s for Real;

theorem Th4:
  for a, b being object holds <*a,b*> = (1,2) --> (a,b)
proof
  let a, b be object;
  set f = (1,2) --> (a,b);
  set g = <*a,b*>;
A1: dom f = {1,2} by FUNCT_4:62;
A2: now
    let x be object;
    assume
A3: x in dom f;
    per cases by A1,A3,TARSKI:def 2;
    suppose
A4:   x = 1;
      hence f.x = a by FUNCT_4:63
        .= g.x by A4;
    end;
    suppose
A5:   x = 2;
      hence f.x = b by FUNCT_4:63
        .= g.x by A5;
    end;
  end;
  dom g = {1,2} by FINSEQ_1:2,89;
  hence thesis by A2,FUNCT_1:2,FUNCT_4:62;
end;
