reserve SBT for Permutation of (8-tuples_on BOOLEAN);
reserve MCFunc for Permutation of
4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN));
reserve MixColumns for
Permutation of 4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN));

theorem LR8D1:
  for D be non empty set, n,m be non zero Element of NAT,
  r be Element of n-tuples_on D st m <= n & 8 <= n-m
  holds Op-Left(Op-Right(r,m),8) is Element of 8-tuples_on D
proof
  let D be non empty set,
  n,m be non zero Element of NAT,
  r be Element of n-tuples_on D;
  assume
A1: m <= n & 8 <= n-m;
  r in { s where s is Element of D*: len s = n};
  then consider s be Element of D* such that
A2: r = s & len s = n;
  len Op-Right(r,m) = n - m by A1,A2,RFINSEQ:def 1;
  then len(Op-Left(Op-Right(r,m),8)) = 8 by A1,FINSEQ_1:59;
  hence thesis by FINSEQ_2:92;
end;
