reserve i,j for Nat;
reserve x,y for set;
reserve A for non empty set;
reserve c for Element of StandardStackSystem A;
reserve m for stack of StandardStackSystem A;
reserve X for non empty non void StackSystem;
reserve s,s1,s2 for stack of X;
reserve e,e1,e2 for Element of X;
reserve X for StackAlgebra;
reserve s,s1,s2,s3 for stack of X;
reserve e,e1,e2,e3 for Element of X;

theorem Th34:
  for S being stack of X/== ex s st S = Class(==_X, s)
  proof
    let S be stack of X/==;
    the carrier' of X/== = Class(==_X)by Def20; then
    S in Class(==_X); then
    ex x being object
      st x in the carrier' of X & S = Class(==_X,x) by EQREL_1:def 3;
    hence thesis;
  end;
