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 Th26:
  len m >= 4 implies IDEAoperationA(m,k,n).1 is_expressible_by n &
  IDEAoperationA(m,k,n).2 is_expressible_by n & IDEAoperationA(m,k,n).3
  is_expressible_by n & IDEAoperationA(m,k,n).4 is_expressible_by n
proof
  assume
A1: len m >= 4;
  then 1 <= len m by XXREAL_0:2;
  then 1 in Seg len m by FINSEQ_1:1;
  then 1 in dom m by FINSEQ_1:def 3;
  then
A2: IDEAoperationA(m,k,n).1 = MUL_MOD(m.1, k.1, n) by Def11;
  3 <= len m by A1,XXREAL_0:2;
  then 3 in Seg len m by FINSEQ_1:1;
  then 3 in dom m by FINSEQ_1:def 3;
  then
A3: IDEAoperationA(m,k,n).3 = ADD_MOD(m.3, k.3, n) by Def11;
  2 <= len m by A1,XXREAL_0:2;
  then 2 in Seg len m by FINSEQ_1:1;
  then 2 in dom m by FINSEQ_1:def 3;
  then
A4: IDEAoperationA(m,k,n).2 = ADD_MOD(m.2, k.2, n) by Def11;
  4 in Seg len m by A1,FINSEQ_1:1;
  then 4 in dom m by FINSEQ_1:def 3;
  then IDEAoperationA(m,k,n).4 = MUL_MOD(m.4, k.4, n) by Def11;
  hence thesis by A2,A4,A3,Th15,Th24;
end;
