reserve a,b,r for non unit non zero Real;
reserve X for non empty set,
        x for Tuple of 4,X;

theorem
  pi_1342(x) = pi_34(pi_23(x)) &
  pi_1423(x) = pi_34(pi_24(x)) &
  pi_2143(x) = pi_12(pi_34(x)) &
  pi_2314(x) = pi_23(pi_12(x)) &
  pi_2341(x) = pi_34(pi_23(pi_12(x))) &
  pi_2413(x) = pi_34(pi_24(pi_12(x))) &
  pi_2431(x) = pi_24(pi_12(x)) &
  pi_3124(x) = pi_23(pi_13(x)) &
  pi_3142(x) = pi_24(pi_34(pi_13(x))) &
  pi_3241(x) = pi_34(pi_13(x)) &
  pi_3412(x) = pi_24(pi_13(x)) &
  pi_3421(x) = pi_24(pi_23(pi_13(x))) &
  pi_4123(x) = pi_23(pi_34(pi_14(x))) &
  pi_4132(x) = pi_24(pi_14(x)) &
  pi_4213(x) = pi_34(pi_14(x)) &
  pi_4312(x) = pi_23(pi_24(pi_14(x))) &
  pi_4321(x) = pi_23(pi_14(x));
