let I be No-StopCode Program of SCMPDS ; :: thesis: for s being State of SCMPDS
for k being Element of NAT st I is_closed_on s & I is_halting_on s & k < LifeSpan (s +* (Initialized (stop I))) holds
CurInstr (Computation (s +* (Initialized (stop I))),k) <> halt SCMPDS
let s be State of SCMPDS ; :: thesis: for k being Element of NAT st I is_closed_on s & I is_halting_on s & k < LifeSpan (s +* (Initialized (stop I))) holds
CurInstr (Computation (s +* (Initialized (stop I))),k) <> halt SCMPDS
let k be Element of NAT ; :: thesis: ( I is_closed_on s & I is_halting_on s & k < LifeSpan (s +* (Initialized (stop I))) implies CurInstr (Computation (s +* (Initialized (stop I))),k) <> halt SCMPDS )
set IsI = Initialized (stop I);
set ss = s +* (Initialized (stop I));
set s2 = Computation (s +* (Initialized (stop I))),k;
assume A1: ( I is_closed_on s & I is_halting_on s & k < LifeSpan (s +* (Initialized (stop I))) ) ; :: thesis: CurInstr (Computation (s +* (Initialized (stop I))),k) <> halt SCMPDS
A2: Initialized (stop I) c= s +* (Initialized (stop I)) by FUNCT_4:26;
I c= Initialized (stop I) by Th17;
then I c= s +* (Initialized (stop I)) by A2, XBOOLE_1:1;
then A3: I c= Computation (s +* (Initialized (stop I))),k by AMI_1:81;
A4: IC (Computation (s +* (Initialized (stop I))),k) in dom I by A1, Th40;
then CurInstr (Computation (s +* (Initialized (stop I))),k) = I . (IC (Computation (s +* (Initialized (stop I))),k)) by A3, GRFUNC_1:8;
hence CurInstr (Computation (s +* (Initialized (stop I))),k) <> halt SCMPDS by A4, SCMPDS_5:def 3; :: thesis: verum