
theorem
  for R being Abelian left_zeroed right_zeroed add-cancelable
  add-associative left_unital commutative associative distributive non empty
doubleLoopStr, I being add-closed left-ideal right-ideal non empty Subset of
  R, J being add-closed left-ideal non empty Subset of R st I,J are_co-prime
  holds I *' J = I /\ J
proof
  let R be left_zeroed right_zeroed add-cancelable add-associative Abelian
  commutative associative distributive left_unital non empty doubleLoopStr, I
  be add-closed left-ideal right-ideal non empty Subset of R, J be add-closed
  left-ideal non empty Subset of R;
A1: I *' J c= I /\ J by Th79;
  assume I,J are_co-prime;
  then
A2: I /\ J c= (I + J) *' (I /\ J) by Th83;
  (I + J) *' (I /\ J) c= I *' J by Th81;
  then I /\ J c= I *' J by A2;
  hence thesis by A1;
end;
