reserve J,J1,K for Element of Segm 13,
  b,b1,b2,c,c1,c2 for Element of SCM+FSA-Data-Loc,
  f,f1,f2 for Element of SCM+FSA-Data*-Loc;
reserve k for Nat,
  J,K,L for Element of Segm 13,
  O,P,R for Element of Segm 9;
reserve da for Int-Location,
  fa for FinSeq-Location,
  x,y for set;
reserve la,lb for Nat,
  La for Nat,
  i for Instruction of SCM+FSA,
  I for Instruction of SCM,
  l for Nat,
  LA,LB for Nat,
  dA,dB,dC,dD for Element of SCM+FSA-Data-Loc,
  DA,DB,DC for Element of SCM-Data-Loc,
  fA,fB,fC for Element of SCM+FSA-Data*-Loc,
  f,g for FinSeq-Location,
  A,B for Data-Location,
  a,b,c,db for Int-Location;
reserve S for State of SCM,
  s,s1 for State of SCM+FSA;

theorem Th71:
  for I being Instruction of SCM+FSA st ex s st Exec(I,s).IC
  SCM+FSA = IC s + 1 holds I is non halting
proof
  let I be Instruction of SCM+FSA;
  given s such that
A1: Exec(I,s).IC SCM+FSA = IC s + 1;
  reconsider T = s as SCM+FSA-State by CARD_3:107;
  IC T = T.NAT;
  then reconsider w = T.NAT as Nat;
  assume I is halting;
  then
A2: Exec(I,s).IC SCM+FSA = T.NAT by Th1;
  Exec(I,s).IC SCM+FSA = w+1 by A1,SCMFSA_1:5,SUBSET_1:def 8;
  hence contradiction by A2;
end;
