
theorem Th86:
  for L being bounded LATTICE st L is Heyting & for x being
  Element of L holds 'not' 'not' x = x for x being Element of L holds 'not' x
  is_a_complement_of x
proof
  let L be bounded LATTICE such that
A1: L is Heyting and
A2: for x being Element of L holds 'not' 'not' x = x;
  let x be Element of L;
A3: 'not' (x "\/" 'not' x) = 'not' x "/\" 'not' 'not' x by A1,Th78
    .= x "/\" 'not' x by A2;
A4: 'not' x >= 'not' x by ORDERS_2:1;
  then x "/\" 'not' x = Bottom L by A1,Th82;
  hence x "\/" 'not' x = 'not' (Bottom L) by A2,A3
    .= Top L by A1,Th80;
  thus thesis by A1,A4,Th82;
end;
