reserve i,j,k,n for Nat;
reserve x,y,z for Tuple of n, BOOLEAN;
reserve m,k,k1,k2 for FinSequence of NAT;

theorem Th42:
  for n being non zero Nat,M being FinSequence of NAT,
m,k st M = IDEA_P(k,n).m & len m >= 4 holds len M >= 4 & M.1 is_expressible_by
n & M.2 is_expressible_by n & M.3 is_expressible_by n & M.4 is_expressible_by n
proof
  let n be non zero Nat, M be FinSequence of NAT,m,k;
  assume that
A1: M = IDEA_P(k,n).m and
A2: len m >= 4;
A3: len m = len IDEAoperationB(m,k,n) by Def12
    .= len IDEAoperationC(IDEAoperationB(m,k,n)) by Def13;
  M = IDEAoperationA(IDEAoperationC(IDEAoperationB(m,k,n)),k,n) by A1,Def15;
  hence thesis by A2,A3,Def11,Th26;
end;
