reserve a,b,c for Integer;

theorem Th1:
  a divides b & a divides b + c implies a divides c
proof
  given u being Integer such that
A1: b = a * u;
  given t being Integer such that
A2: b + c = a * t;
  c = a*(t - u) by A1,A2;
  hence thesis;
end;
