reserve L, j, k, l, m, n, p, q for Nat,
  A for Data-Location,
  I for Instruction of SCM;
reserve i for Instruction of SCM+FSA;

theorem
 not InsCode i in {6,7,8} implies IncAddr(i,k) = i
proof
 assume not InsCode i in {6,7,8};
  then
A1: InsCode i <> 6 & InsCode i <> 7 & InsCode i <> 8 by ENUMSET1:def 1;
  InsCode i = 0 or ... or InsCode i = 12 by SCMFSA_2:16;
  then per cases by A1;
  suppose InsCode i = 0;
    then i = halt SCM+FSA by SCMFSA_2:95;
   hence thesis by COMPOS_0:4;
  end;
  suppose
    InsCode i = 1;
    then consider da,db being Int-Location such that
A2: i = da := db by SCMFSA_2:30;
   thus thesis by A2,COMPOS_0:4;
  end;
  suppose
    InsCode i = 2;
    then consider da,db being Int-Location such that
A3: i = AddTo(da, db) by SCMFSA_2:31;
    thus thesis by A3,COMPOS_0:4;
  end;
  suppose
    InsCode i = 3;
    then consider da,db being Int-Location such that
A4: i = SubFrom(da, db) by SCMFSA_2:32;
    thus thesis by A4,COMPOS_0:4;
  end;
  suppose
    InsCode i = 4;
    then consider da,db being Int-Location such that
A5: i = MultBy(da, db) by SCMFSA_2:33;
    thus thesis by A5,COMPOS_0:4;
  end;
  suppose
    InsCode i = 5;
    then consider da,db being Int-Location such that
A6: i = Divide(da, db) by SCMFSA_2:34;
    thus thesis by A6,COMPOS_0:4;
  end;
  suppose
    InsCode i = 9;
    then consider db,da being Int-Location, f being FinSeq-Location such that
A7: i = da :=(f, db) by SCMFSA_2:38;
    thus thesis by A7,COMPOS_0:4;
  end;
  suppose
    InsCode i = 10;
    then consider db,da being Int-Location, f being FinSeq-Location such that
A8: i = (f, db):=da by SCMFSA_2:39;
    thus thesis by A8,COMPOS_0:4;
  end;
  suppose
    InsCode i = 11;
    then consider da being Int-Location, f being FinSeq-Location such that
A9: i = da :=len f by SCMFSA_2:40;
    thus thesis by A9,COMPOS_0:4;
  end;
  suppose
    InsCode i = 12;
    then consider da being Int-Location, f being FinSeq-Location such that
A10: i = f:=<0,...,0>da by SCMFSA_2:41;
   thus thesis by A10,COMPOS_0:4;
  end;
 end;
