theorem
  for X being proper-for-identity StackAlgebra holds
  X, StandardStackSystem the carrier of X are_isomorphic
  proof
    let X be proper-for-identity StackAlgebra;
    consider G such that
    (for s being stack of X holds G.s = |.s.|) and
A1: id the carrier of X, G form_isomorphism_between
    X, StandardStackSystem the carrier of X by Th48;
    take id the carrier of X, G;
    thus thesis by A1;
  end;
