reserve F for total
  NAT-defined (the InstructionsF of SCM)-valued Function;

theorem
  for F being total
   NAT-defined (the InstructionsF of SCM)-valued Function
    st <%SCM-goto 1%>^<%halt SCM%> c= F
  for i1, i2 being Integer,
      s being 0-started State-consisting of <%i1,i2%>
    holds F halts_on s &
 LifeSpan(F,s) = 1 & for d
  being Data-Location holds (Result(F,s)).d = s.d
proof
  let F being total
   NAT-defined (the InstructionsF of SCM)-valued Function such that
A1: <%SCM-goto 1%>^<%halt SCM%> c= F;
  let i1, i2 be Integer,
      s be 0-started State-consisting of <%i1,i2%>;
  set s1 = Comput(F,s,0+1);
A2: IC s = 0 & s = Comput(F,s,0) by EXTPRO_1:2,MEMSTR_0:def 11;
A3: F.0 = SCM-goto 1 by A1,Th3;
  then
A4: IC s1 = (0+1) by A2,Th9;
A5: F.1 = halt SCM by A1,Th3;
  hence F halts_on s by A4,EXTPRO_1:30;
  thus LifeSpan(F,s) = 1 by A5,A2,A4,EXTPRO_1:33;
  let d be Data-Location;
  thus (Result(F,s)).d = s1.d by A5,A4,EXTPRO_1:7
    .= s.d by A3,A2,Th9;
end;
