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 Th7:
  not emp s implies |.pop s.| = Del(|.s.|,1)
  proof
    assume not emp s; then
    |.s.| = <*top s*>^|.pop s.| by Th6;
    hence thesis by WSIERP_1:40;
  end;
