reserve L for Ortholattice,
  a, b, c for Element of L;

theorem
  L is orthomodular iff for a,b holds a "/\" (a` "\/" (a "/\" b)) = a "/\" b
proof
  thus L is orthomodular implies for a,b holds a "/\" (a` "\/" (a "/\" b)) = a
  "/\" b
  by LATTICES:6,Th34;
  assume
A1: for a,b holds a "/\" (a` "\/" (a "/\" b)) = a "/\" b;
  for a,b holds b [= a implies a "/\" (a` "\/" b) = b
  proof
    let a,b;
    assume
A2: b [= a;
    hence b = a "/\" b by LATTICES:4
      .= a "/\" (a` "\/" (a "/\" b)) by A1
      .= a "/\" (a` "\/" b) by A2,LATTICES:4;
  end;
  hence thesis by Th34;
end;
