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 Th26:
  emp s implies core s = s
  proof set R = ConstructionRed X;
    assume
A1: emp s;
    consider t being the carrier' of X-valued RedSequence of R such that
A2: t.1 = s & t.len t = core s and
A3: for i st 1 <= i & i < len t holds not emp t/.i & t/.(i+1) = pop(t/.i)
    by Def19;
A4: 1 in dom t by FINSEQ_5:6; then
    t/.1 = t.1 by PARTFUN1:def 6; then
    1 <= len t & len t <= 1 by A1,A2,A3,A4,FINSEQ_3:25;
    hence thesis by A2,XXREAL_0:1;
  end;
