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 Th14:
  s1 == s2 & emp s1 implies emp s2
  proof
    assume
A1: |.s1.| = |.s2.| & emp s1;
    assume not emp s2; then
    |.s2.| = <*top s2*>^|.pop s2.| by Th6;
    hence thesis by A1,Th5;
  end;
