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 Th18:
  s1 == s2 & not emp s1 implies top s1 = top s2
  proof
    assume
A1: s1 == s2 & not emp s1; then
A2: |.s1.| = |.s2.| & not emp s2 by Th14;
    thus top s1 = |.s1.|.1 by A1,Th9 .= top s2 by A2,Th9;
  end;
