reserve L for Boolean non empty RelStr;
reserve a,b,c,d for Element of L;

theorem
  (a"/\"b) "\/" (b"/\"c) "\/" (c"/\"a) = (a"\/"b) "/\" (b"\/"c) "/\" (c
  "\/" a )
proof
  (a"/\"b) "\/" (b"/\"c) "\/" (c"/\"a) = ((a"\/"(b"/\"c)) "/\" (b"\/"(b
  "/\"c))) "\/" (c"/\"a) by WAYBEL_1:5
    .= ((a"\/"(b"/\"c)) "/\" b) "\/" (c"/\"a) by LATTICE3:17
    .= ((a"\/"(b"/\"c)) "\/" (c"/\"a)) "/\" (b "\/" (c"/\"a)) by WAYBEL_1:5
    .= ((a"\/"(b"/\"c)) "\/" (c"/\"a)) "/\" ((b"\/"c) "/\" (b"\/" a)) by
WAYBEL_1:5
    .= ((b"/\"c)"\/"(a"\/"(c"/\"a))) "/\" ((b"\/"c) "/\" (b"\/" a)) by
LATTICE3:14
    .= ((b"/\"c)"\/"a) "/\" ((b"\/"c) "/\" (b"\/"a)) by LATTICE3:17
    .= ((b"\/"a) "/\" (c"\/"a)) "/\" ((b"\/"c) "/\" (b"\/"a)) by WAYBEL_1:5
    .= (b"\/"a) "/\" (((c"\/"a) "/\" (b"\/"a)) "/\" (b"\/"c)) by LATTICE3:16
    .= (b"\/"a) "/\" ( (b"\/"a) "/\" ((c"\/"a) "/\" (b"\/"c))) by LATTICE3:16
    .= ((b"\/"a) "/\" (b"\/"a)) "/\" ((c"\/"a) "/\" (b"\/"c)) by LATTICE3:16
    .= (b"\/"a) "/\" ((c"\/"a) "/\" (b"\/"c)) by Th2
    .= ((a"\/"b) "/\" (b"\/"c)) "/\" (c"\/"a) by LATTICE3:16;
  hence thesis;
end;
