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
for k being Element of NAT st CurInstr (Computation s,k) = halt S holds
Computation s,(LifeSpan s) = Computation s,k
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
for k being Element of NAT st CurInstr (Computation s,k) = halt S holds
Computation s,(LifeSpan s) = Computation s,k
let s be State of S; :: thesis: for k being Element of NAT st CurInstr (Computation s,k) = halt S holds
Computation s,(LifeSpan s) = Computation s,k
let k be Element of NAT ; :: thesis: ( CurInstr (Computation s,k) = halt S implies Computation s,(LifeSpan s) = Computation s,k )
assume A1: CurInstr (Computation s,k) = halt S ; :: thesis: Computation s,(LifeSpan s) = Computation s,k
IC (Computation s,k) in NAT by Def4;
then X: IC (Computation s,k) in dom (ProgramPart s) by LmU;
(ProgramPart s) . (IC (Computation s,k)) = CurInstr (Computation s,k) by LmX;
then A2: ProgramPart s halts_on s by Def20, X, A1;
set Ls = LifeSpan s;
A3: CurInstr (Computation s,(LifeSpan s)) = halt S by A2, Def46;
LifeSpan s <= k by A1, A2, Def46;
hence Computation s,(LifeSpan s) = Computation s,k by A3, Th52; :: thesis: verum