let s be State of SCMPDS ; :: thesis: for I being parahalting No-StopCode Program of SCMPDS
for k being Element of NAT st Initialized I c= s & k < LifeSpan (s +* (Initialized (stop I))) holds
CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) <> halt SCMPDS
let I be parahalting No-StopCode Program of SCMPDS ; :: thesis: for k being Element of NAT st Initialized I c= s & k < LifeSpan (s +* (Initialized (stop I))) holds
CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) <> halt SCMPDS
let k be Element of NAT ; :: thesis: ( Initialized I c= s & k < LifeSpan (s +* (Initialized (stop I))) implies CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) <> halt SCMPDS )
set sI = s +* (Initialized (stop I));
set s1 = Comput (ProgramPart s),s,k;
set s2 = Comput (ProgramPart (s +* (Initialized (stop I)))),(s +* (Initialized (stop I))),k;
assume that
A1: Initialized I c= s and
A2: k < LifeSpan (s +* (Initialized (stop I))) ; :: thesis: CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) <> halt SCMPDS
A3: I c= Comput (ProgramPart s),s,k by A1, AMI_1:81, SCMPDS_4:57;
A4: IC (Comput (ProgramPart (s +* (Initialized (stop I)))),(s +* (Initialized (stop I))),k) in dom I by A2, Th28;
Y: (ProgramPart (Comput (ProgramPart s),s,k)) /. (IC (Comput (ProgramPart s),s,k)) = (Comput (ProgramPart s),s,k) . (IC (Comput (ProgramPart s),s,k)) by AMI_1:150;
CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) = (Comput (ProgramPart s),s,k) . (IC (Comput (ProgramPart (s +* (Initialized (stop I)))),(s +* (Initialized (stop I))),k)) by A1, A2, Th29, AMI_1:121, Y
.= I . (IC (Comput (ProgramPart (s +* (Initialized (stop I)))),(s +* (Initialized (stop I))),k)) by A3, A4, GRFUNC_1:8 ;
hence CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) <> halt SCMPDS by A4, Def3; :: thesis: verum