
theorem Th30: :: 4.34
  for L being join-commutative join-associative Huntington non
empty ComplLLattStr, a, b, c being Element of L
 holds a *' (b + c) = (a *' b) + (a *' c)
proof
  let L be join-commutative join-associative Huntington non empty
  ComplLLattStr, a, b, c be Element of L;
  (a *' b) + (a *' c) + (a *' (b + c))` = Top L & ((a *' b) + (a *' c)) *'
  (a *' (b + c))` = Bot L by Th28,Th29;
  then ((a *' b) + (a *' c))` = (a *' (b + c))` by Th23;
  hence thesis by Th10;
end;
