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

theorem Th11:
  for n,m,l st n divides m & n divides m +^ l holds n divides l
proof
  let n,m,l;
  assume n divides m;
  then consider a such that
A1: m = n*^a by Th5;
  assume n divides m +^ l;
  then consider b such that
A2: m +^ l = n*^b by Th5;
  assume
A3: not n divides l;
  l = n*^b -^ n*^a by A1,A2,ORDINAL3:52
    .= (b-^a)*^n by ORDINAL3:63;
  hence thesis by A3;
end;
