reserve m for Nat;
reserve P,PP,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem Th6:
  for s being State of SCM+FSA, i being Instruction of SCM+FSA st
  InsCode i in {0,6,7,8} holds DataPart Exec(i,s) = DataPart s
proof
  let s be State of SCM+FSA;
  let i be Instruction of SCM+FSA;
  assume
A1: InsCode i in {0,6,7,8};
  now
    let a be Int-Location;
    let f be FinSeq-Location;
    per cases by A1,ENUMSET1:def 2;
    suppose
      InsCode i = 0;
      then i = halt SCM+FSA by SCMFSA_2:95;
      hence Exec(i,s).a = s.a & Exec(i,s).f = s.f by EXTPRO_1:def 3;
    end;
    suppose
      InsCode i = 6;
      then ex lb being Nat st i = goto lb by SCMFSA_2:35;
      hence Exec(i,s).a = s.a & Exec(i,s).f = s.f by SCMFSA_2:69;
    end;
    suppose
      InsCode i = 7;
      then
      ex lb being Nat, b being Int-Location st
      i = b=0_goto lb by SCMFSA_2:36;
      hence Exec(i,s).a = s.a & Exec(i,s).f = s.f by SCMFSA_2:70;
    end;
    suppose
      InsCode i = 8;
      then
      ex lb being Nat, b being Int-Location st
      i = b>0_goto lb by SCMFSA_2:37;
      hence Exec(i,s).a = s.a & Exec(i,s).f = s.f by SCMFSA_2:71;
    end;
  end;
  hence thesis by SCMFSA_M:2;
end;
