let p be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being InitHalting Program of SCM+FSA st Initialize ((intloc 0) .--> 1) c= s & I c= p holds
for k being Element of NAT st k <= LifeSpan (p,s) holds
CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) <> halt SCM+FSA
let s be State of SCM+FSA; :: thesis: for I being InitHalting Program of SCM+FSA st Initialize ((intloc 0) .--> 1) c= s & I c= p holds
for k being Element of NAT st k <= LifeSpan (p,s) holds
CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) <> halt SCM+FSA
let I be InitHalting Program of SCM+FSA; :: thesis: ( Initialize ((intloc 0) .--> 1) c= s & I c= p implies for k being Element of NAT st k <= LifeSpan (p,s) holds
CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) <> halt SCM+FSA )
set s2 = s;
set p2 = p +* (loop I);
assume A1: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: ( not I c= p or for k being Element of NAT st k <= LifeSpan (p,s) holds
CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) <> halt SCM+FSA )
assume A2: I c= p ; :: thesis: for k being Element of NAT st k <= LifeSpan (p,s) holds
CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) <> halt SCM+FSA
A3: p halts_on s by Def2, A1, A2;

hereby :: thesis: verum

let k be Element of NAT ; :: thesis: ( k <= LifeSpan (p,s) implies not CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) = halt SCM+FSA )
set lk = IC (Comput (p,s,k));
A4: ( IC (Comput (p,s,k)) in dom I & dom I = dom (loop I) ) by A1, Def1, A2, FUNCT_4:99;
then A5: (loop I) . (IC (Comput (p,s,k))) in rng (loop I) by FUNCT_1:def 3;
assume k <= LifeSpan (p,s) ; :: thesis: not CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) = halt SCM+FSA
then IC (Comput (p,s,k)) = IC (Comput ((p +* (loop I)),s,k)) by A1, A3, Th55, A2;
then A6: CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) = (p +* (loop I)) . (IC (Comput (p,s,k))) by PBOOLE:143
.= (loop I) . (IC (Comput (p,s,k))) by A4, FUNCT_4:13 ;
assume CurInstr ((p +* (loop I)),(Comput ((p +* (loop I)),s,k))) = halt SCM+FSA ; :: thesis: contradiction
hence contradiction by A6, A5, SCMFSA8C:75; :: thesis: verum

end;