 reserve X,Y,Z,E,F,G,S,T for RealLinearSpace;

theorem LemmaA:
  for s being Element of product <*E,F*>,
      i being Element of dom <*E,F*>,
      x1 being object holds
  len(s +* (i,x1)) = 2
  proof
    let s be Element of product <*E,F*>,
        i be Element of dom <*E,F*>,
        x1 be object;
    consider x be Point of E, y be Point of F such that
    A3: s = <*x,y*> by PRVECT_3:14;
    A1: len s = 2 by A3,FINSEQ_1:44;
    dom(s +* (i,x1)) = dom s by FUNCT_7:30
        .= Seg 2 by A1,FINSEQ_1:def 3;
    hence thesis by FINSEQ_1:def 3;
  end;
