reserve G for Robbins join-associative join-commutative non empty
  ComplLLattStr;
reserve x, y, z, u, v for Element of G;

theorem Th59:
  for L being well-complemented join-commutative meet-commutative
non empty OrthoLattStr, x being Element of L holds x + x` = Top L & x "/\" x`
  = Bottom L
proof
  let L be well-complemented join-commutative meet-commutative non empty
  OrthoLattStr, x be Element of L;
A1: x` is_a_complement_of x by Def10;
  hence x + x` = Top L;
  thus thesis by A1;
end;
