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
  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 implies IDEAoperationC(m).1
is_expressible_by n & IDEAoperationC(m).2 is_expressible_by n & IDEAoperationC(
  m).3 is_expressible_by n & IDEAoperationC(m).4 is_expressible_by n
proof
  assume that
A1: len m >= 4 and
A2: m.1 is_expressible_by n & m.2 is_expressible_by n & m.3
  is_expressible_by n & m.4 is_expressible_by n;
  1 <= len m by A1,XXREAL_0:2;
  then 1 in Seg len m by FINSEQ_1:1;
  then
A3: 1 in dom m by FINSEQ_1:def 3;
  3 <= len m by A1,XXREAL_0:2;
  then 3 in Seg len m by FINSEQ_1:1;
  then
A4: 3 in dom m by FINSEQ_1:def 3;
  2 <= len m by A1,XXREAL_0:2;
  then 2 in Seg len m by FINSEQ_1:1;
  then
A5: 2 in dom m by FINSEQ_1:def 3;
  4 in Seg len m by A1,FINSEQ_1:1;
  then 4 in dom m by FINSEQ_1:def 3;
  hence thesis by A2,A3,A5,A4,Lm3,Lm4,Lm5;
end;
