let j be Element of NAT ; :: thesis: for N being non empty with_non-empty_elements set
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 LifeSpan s <= j & ProgramPart s halts_on s holds
Comput (ProgramPart s),s,j = Comput (ProgramPart s),s,(LifeSpan s)
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 LifeSpan s <= j & ProgramPart s halts_on s holds
Comput (ProgramPart s),s,j = 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 LifeSpan s <= j & ProgramPart s halts_on s holds
Comput (ProgramPart s),s,j = Comput (ProgramPart s),s,(LifeSpan s)
let s be State of S; :: thesis: ( LifeSpan s <= j & ProgramPart s halts_on s implies Comput (ProgramPart s),s,j = Comput (ProgramPart s),s,(LifeSpan s) )
assume that
A1: LifeSpan s <= j and
A2: ProgramPart s halts_on s ; :: thesis: Comput (ProgramPart s),s,j = Comput (ProgramPart s),s,(LifeSpan s)
X: ProgramPart (Comput (ProgramPart s),s,(LifeSpan s)) = ProgramPart s by LmY;
CurInstr (ProgramPart (Comput (ProgramPart s),s,(LifeSpan s))),(Comput (ProgramPart s),s,(LifeSpan s)) = halt S by A2, Def46;
hence Comput (ProgramPart s),s,j = Comput (ProgramPart s),s,(LifeSpan s) by A1, Th52, X; :: thesis: verum