
theorem
  for L being non empty 1-sorted, N being non empty reflexive NetStr
over L for i, x being Element of N, x1 being Element of N|i st x = x1 holds N.x
  = (N|i).x1
proof
  let L be non empty 1-sorted, N be non empty reflexive NetStr over L, i, x be
  Element of N, x1 be Element of N|i;
  assume x = x1;
  hence N.x = ((the mapping of N)|(the carrier of N|i)).x1 by FUNCT_1:49
    .= (N|i).x1 by Def7;
end;
