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 Th15:
  emp s1 & emp s2 implies s1 == s2
  proof
    assume emp s1 & emp s2; then
    |.s1.| = {} & |.s2.| = {} by Th5;
    hence |.s1.| = |.s2.|;
  end;
