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

theorem
  for R being Relation st not ex a,b being object st a,b are_critical_wrt R
  holds R is locally-confluent
proof
  let R be Relation such that
A1: not ex a,b being object st a,b are_critical_wrt R;
  let a,b,c be object;
  assume [a,b] in R & [a,c] in R;
  then
A2: b,c are_divergent<=1_wrt R;
  not b,c are_critical_wrt R by A1;
  hence thesis by A2;
end;
