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

theorem
  for A being RelStr, B, C being Subset of A,
    s being FinSequence of A
  st s is B-desc_ordering & C c= B holds
    ex s2 being FinSequence of A st s2 is C-desc_ordering
proof
  let A be RelStr, B, C be Subset of A;
  let s be FinSequence of A;
  assume that
    A1: s is B-desc_ordering and
    A2: C c= B;
  Rev(Rev(s)) is B-desc_ordering by A1;
  then Rev(s) is B-asc_ordering by Th75;
  then consider s2 being FinSequence of A such that
    A3: s2 is C-asc_ordering by A2, Th80;
  take Rev(s2);
  thus thesis by A3, Th75;
end;
