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

theorem LemmaA:
  for s being Point of product <*E,F*>,
      i being Element of dom <*E,F*>,
      x1 being object holds
  len(s +* (i,x1)) = 2
  proof
    let s be Point 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_3:19;
A1: len s = 2 by FINSEQ_1:44,A3;
    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;
