let s be State of SCMPDS ; :: thesis: ( ProgramPart s halts_on s implies for k being Element of NAT st LifeSpan s <= k holds
CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) = halt SCMPDS )
assume ProgramPart s halts_on s ; :: thesis: for k being Element of NAT st LifeSpan s <= k holds
CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) = halt SCMPDS
then A1: CurInstr (ProgramPart (Comput (ProgramPart s),s,(LifeSpan s))),(Comput (ProgramPart s),s,(LifeSpan s)) = halt SCMPDS by AMI_1:def 46;
TX: ProgramPart s = ProgramPart (Comput (ProgramPart s),s,(LifeSpan s)) by AMI_1:144;
let k be Element of NAT ; :: thesis: ( LifeSpan s <= k implies CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) = halt SCMPDS )
assume LifeSpan s <= k ; :: thesis: CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) = halt SCMPDS
then Comput (ProgramPart s),s,(LifeSpan s) = Comput (ProgramPart s),s,k by A1, AMI_1:52, TX;
hence CurInstr (ProgramPart (Comput (ProgramPart s),s,k)),(Comput (ProgramPart s),s,k) = halt SCMPDS by A1; :: thesis: verum