reserve G for RealNormSpace-Sequence;

theorem Th7:
  for x be VECTOR of product G, y be Element of product carr G st
    x = y holds ||.x.|| = |.normsequence(G,y).|
proof
  let x be VECTOR of product G;
  let y be Element of product carr G;
  assume
A1: x=y;
  product G = NORMSTR(# product carr G,zeros G,[:addop G:], [:multop G:],
    productnorm G #) by Th6;
  hence thesis by A1,Def12;
end;
