let l be Instruction-Location of SCM+FSA ; :: thesis: for s being State of st IC s = l & s . l = goto l holds
not ProgramPart s halts_on s
let s be State of ; :: thesis: ( IC s = l & s . l = goto l implies not ProgramPart s halts_on s )
set S = s;
assume that
A1: IC s = l and
A2: s . l = goto l ; :: thesis: not ProgramPart s halts_on s
defpred S₁[ Element of NAT ] means Computation s,$1 = s;
A3: for m being Element of NAT st S₁[m] holds
S₁[m + 1]

proof

let m be Element of NAT ; :: thesis: ( S₁[m] implies S₁[m + 1] )
A4: ( ( for f being FinSeq-Location holds (Exec (goto l),s) . f = s . f ) & ( for i being Instruction-Location of SCM+FSA holds (Exec (goto l),s) . i = s . i ) ) by AMI_1:def 13, SCMFSA_2:95;
A5: ( IC (Exec (goto l),s) = IC s & ( for a being Int-Location holds (Exec (goto l),s) . a = s . a ) ) by A1, SCMFSA_2:95;
assume Computation s,m = s ; :: thesis: S₁[m + 1]
hence Computation s,(m + 1) = Following s by AMI_1:14
.= s by A1, A2, A5, A4, SCMFSA_2:86 ;
:: thesis: verum

end;

let m be Element of NAT ; :: according to AMI_1:def 20 :: thesis: ( not IC (Computation s,m) in dom (ProgramPart s) or not (ProgramPart s) . (IC (Computation s,m)) = halt SCM+FSA )
A6: S₁[ 0 ] by AMI_1:13;
A7: for m being Element of NAT holds S₁[m] from NAT_1:sch 1(A6, A3);
assume IC (Computation s,m) in dom (ProgramPart s) ; :: thesis: not (ProgramPart s) . (IC (Computation s,m)) = halt SCM+FSA
CurInstr s = goto l by A1, A2;
then X: CurInstr (Computation s,m) = goto l by A7;
InsCode (goto l) = 6 by SCMFSA_2:47;
then CurInstr (Computation s,m) <> halt SCM+FSA by X, SCMFSA_2:124;
hence (ProgramPart s) . (IC (Computation s,m)) <> halt SCM+FSA by SCMFSA_2:47, SCMFSA_2:124, X, AMI_1:145; :: thesis: verum