let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N
for s being State of S st ProgramPart s halts_on s holds
Result s = Comput (ProgramPart s),s,(LifeSpan s)
let S be non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N; :: thesis: for s being State of S st ProgramPart s halts_on s holds
Result s = Comput (ProgramPart s),s,(LifeSpan s)
let s be State of S; :: thesis: ( ProgramPart s halts_on s implies Result s = Comput (ProgramPart s),s,(LifeSpan s) )
assume A1: ProgramPart s halts_on s ; :: thesis: Result s = Comput (ProgramPart s),s,(LifeSpan s)
then A2: CurInstr (ProgramPart (Comput (ProgramPart s),s,(LifeSpan s))),(Comput (ProgramPart s),s,(LifeSpan s)) = halt S by Def46;
consider m being Element of NAT such that
A3: Result s = Comput (ProgramPart s),s,m and
A4: CurInstr (ProgramPart (Result s)),(Result s) = halt S by A1, Def22;
Y: ProgramPart (Comput (ProgramPart s),s,(LifeSpan s)) = ProgramPart s by LmY;
LifeSpan s <= m by A1, A3, A4, Def46;
hence Result s = Comput (ProgramPart s),s,(LifeSpan s) by A2, A3, Th52, Y; :: thesis: verum