theorem Th18:
  for I being Instruction of SCM R st ex s st Exec(I,s).IC SCM R =
  IC s + 1 holds I is non halting
proof
  let I be Instruction of SCM R;
  given s such that
A1: Exec(I, s).IC SCM R = IC s + 1;
A2: the_Values_of SCM R = (SCM-VAL R)*SCM-OK by Lm1;
  reconsider t = s as SCM-State of R by A2,CARD_3:107;
  IC t = t.NAT;
  then reconsider w = t.NAT as Element of NAT;
A3: Exec(I,s).IC SCM R = w+1 by A1,Def1;
  assume
A4: I is halting;
  IC t = IC s by Def1;
  then Exec(I,s).IC SCM R = t.NAT by A4;
  hence contradiction by A3;
end;
