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

theorem
  for R being Relation, a,b being object st a,b are_convertible_wrt R &
  not a in field R holds a = b
proof
  let R be Relation;
  let a,b be object;
A1: field R = field (R~) & field (R \/ R~) = (field R) \/ field (R~) by
RELAT_1:18,21;
  assume R \/ R~ reduces a,b;
  hence thesis by A1,Th14;
end;
