reserve k for Nat;
reserve N for with_zero set,
   S for IC-recognized
    halting IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N;

theorem Th6:
  for q be non halt-free finite
   (the InstructionsF of S)-valued NAT-defined Function
  for p being q-autonomic non empty FinPartState of S
   holds IC S in dom p
proof
  let q be non halt-free finite
   (the InstructionsF of S)-valued NAT-defined Function;
  let p be q-autonomic non empty FinPartState of S;
A1:  dom p meets {IC S} \/ Data-Locations S by MEMSTR_0:41;
  per cases by A1,XBOOLE_1:70;
  suppose dom p meets {IC S};
    hence thesis by ZFMISC_1:50;
  end;
  suppose dom p meets Data-Locations S;
    then dom p /\ Data-Locations S <> {} by XBOOLE_0:def 7;
    then DataPart p <> {} by RELAT_1:38,61;
    hence thesis by Th3;
  end;
end;
