theorem
  L is modular implies latt F is modular
proof
  assume
A1: for a,b,c being Element of L st a [= c holds a"\/"(b"/\"c) = (a"\/"b
  )"/\"c;
  let a,b,c be Element of latt F such that
A2: a [= c;
  reconsider p = a, q = b, r = c as Element of F by Th49;
  b"/\"c = q"/\"r by Th50;
  then
A3: a"\/"(b"/\"c) = p"\/"(q"/\"r) by Th50;
  a"\/"b = p"\/"q by Th50;
  then
A4: (a"\/"b)"/\"c = (p"\/"q)"/\" r by Th50;
  p [= r by A2,Th51;
  hence a"\/"(b"/\"c) = (a"\/"b)"/\"c by A1,A3,A4;
end;
