reserve X,Z for set;
reserve x,y,z for object;
reserve A,B,C for Subset of X;

theorem
  for A being antisymmetric RelStr, B being Subset of A,
    s1, s2 being FinSequence of A st
      s1 is B-desc_ordering & s2 is B-desc_ordering holds s1 = s2
proof
  let A be antisymmetric RelStr;
  let B be Subset of A;
  let s1, s2 be FinSequence of A;
  assume s1 is B-desc_ordering & s2 is B-desc_ordering;
  then Rev(Rev(s1)) is B-desc_ordering &
    Rev(Rev(s2)) is B-desc_ordering;
  then Rev(s1) is B-asc_ordering & Rev(s2) is B-asc_ordering by Th75;
  then A1: Rev(s1) = Rev(s2) by Th77;
  thus s1 = Rev(Rev(s2)) by A1 .= s2;
end;
