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 Th16:
  s1 == s2 implies push(e,s1) == push(e,s2)
  proof
    assume |.s1.| = |.s2.|;
    hence |.push(e,s1).| = <*e*>^|.s2.| by Th8 .= |.push(e,s2).| by Th8;
  end;
