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;
