reserve A,B,C for Ordinal;
reserve a,b,c,d for natural Ordinal;
reserve l,m,n for natural Ordinal;

theorem Th6:
  for m,n st {} in m holds n mod^ m in m
proof
  let m,n;
  assume {} in m;
  then
A1: ex C st n = (n div^ m)*^m+^C & C in m by ORDINAL3:def 6;
  n mod^ m = n-^(n div^ m)*^m by ORDINAL3:def 7;
  hence thesis by A1,ORDINAL3:52;
end;
