reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

theorem Th20:
  <*a,b,c*> = (1,2,3) --> (a,b,c)
  proof
  set f = (1,2,3) --> (a,b,c);
  set g = <*a,b,c*>;
A1: dom g = Seg len g by FINSEQ_1:def 3
    .= {1,2,3} by FINSEQ_1:45,FINSEQ_3:1;
A2: dom f = {1,2,3} by FUNCT_4:128;
  now
    let x be object;
    assume
A3: x in dom f;
    per cases by A2,A3,ENUMSET1:def 1;
    suppose
A4:   x = 1;
      hence f.x = a by FUNCT_4:134
        .= g.x by A4;
    end;
    suppose
A5:   x = 2;
      hence f.x = b by FUNCT_4:135
        .= g.x by A5;
    end;
    suppose
A6:   x = 3;
      hence f.x = c by FUNCT_4:135
        .= g.x by A6;
    end;
  end;
  hence thesis by A1,FUNCT_4:128,FUNCT_1:2;
end;
