reserve p,q,r for FinSequence,
  x,y for object;

theorem
  for Q being co-well_founded Relation, R being Relation st R c= Q holds
  R is co-well_founded
proof
  let Q be co-well_founded Relation, R be Relation;
  assume
A1: R c= Q;
  let Y be set;
  assume that
A2: Y c= field R and
A3: Y <> {};
  field R c= field Q by A1,RELAT_1:16;
  then Y c= field Q by A2;
  then consider a being object such that
A4: a in Y and
A5: for b being object st b in Y & a <> b holds not [a,b] in Q by A3,Def16;
  take a;
  thus a in Y by A4;
  let b be object;
  assume b in Y & a <> b;
  hence thesis by A1,A5;
end;
