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 Th29:
  core s in coset s
  proof
    consider t being the carrier' of X-valued RedSequence of ConstructionRed X
    such that
A1: t.1 = s & t.len t = core s and
    for i st 1 <= i & i < len t holds not emp t/.i & t/.(i+1) = pop(t/.i)
    by Def19;
    ConstructionRed X reduces s, core s by A1; then
    core s in {s1: ConstructionRed X reduces s,s1};
    hence thesis by Th25;
  end;
