
theorem Th48:
  for F being non degenerated almost_left_invertible commutative
Ring for a,b,c,d being Element of F st b <> 0.F & d <> 0.F holds (a/b) * (c/d)
  = (a * c) / (b * d)
proof
  let F be non degenerated almost_left_invertible commutative Ring;
  let a,b,c,d be Element of F;
  assume
A1: b <> 0.F & d <> 0.F;
  (a/b) * (c/d) = (a * (b" * (c * d"))) by GROUP_1:def 3
    .= (a * ((b" * d") * c)) by GROUP_1:def 3
    .= (a * c) * (b" * d") by GROUP_1:def 3
    .= (a * c) / (d * b) by A1,GCD_1:49;
  hence thesis;
end;
