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 Th36:
  for S being stack of X/== st S = Class(==_X, s) holds emp s iff emp S
  proof
    let S be stack of X/==; assume
A1: S = Class(==_X, s);
    consider s1 such that
A2: emp s1 by Th2;
    emp S iff S in {the s_empty of X} by Def20; then
    emp S iff S = the s_empty of X by TARSKI:def 1; then
    emp S iff S = Class(==_X, s1) by A2,Th19; then
    emp S iff [s,s1] in ==_X by A1,EQREL_1:35; then
    emp S iff s == s1 by Def16;
    hence emp s iff emp S by A2,Th14,Th15;
  end;
