reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem Th11:
  i divides j & i divides h implies i divides j mod h
proof
  assume that
A1: i divides j and
A2: i divides h;
A3: now
    assume h = 0;
    then j mod h = 0 by Def2;
    hence thesis by Th6;
  end;
  now
    assume h <> 0;
    then
A4: j = h * (j div h) + (j mod h) by INT_1:59;
    i divides h * (j div h) by A2,Th9;
    hence thesis by A1,A4,Th10;
  end;
  hence thesis by A3;
end;
