reserve X,Y for set;
reserve R for domRing-like commutative Ring;
reserve c for Element of R;

theorem Th7:
  for R being associative non empty multLoopStr
  for a,b,c being Element of R holds
    a divides b implies a divides b * c
proof
  let R be associative non empty multLoopStr;
  let a,b,c be Element of R;
  assume a divides b;
  then consider d being Element of R such that
A1: a * d = b;
  a * (d * c) = b * c by A1,GROUP_1:def 3;
  hence thesis;
end;
