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

theorem Th53:
  for R being with_UN_property Relation for a,b,c being object st
  b is_a_normal_form_of a,R & c is_a_normal_form_of a,R holds b = c
proof
  let R be with_UN_property Relation;
  let a,b,c be object such that
A1: b is_a_normal_form_wrt R and
A2: R reduces a,b and
A3: c is_a_normal_form_wrt R and
A4: R reduces a,c;
  b,c are_divergent_wrt R by A2,A4;
  then b,c are_convertible_wrt R by Th37;
  hence thesis by A1,A3,Def19;
end;
