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 P being the Instructions of b₁ -valued ManySortedSet of NAT
for s being State of S
for k being Element of NAT st CurInstr P,(Comput P,s,k) = halt S holds
Comput P,s,(LifeSpan P,s) = Comput P,s,k
let S be non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N; :: thesis: for P being the Instructions of S -valued ManySortedSet of NAT
for s being State of S
for k being Element of NAT st CurInstr P,(Comput P,s,k) = halt S holds
Comput P,s,(LifeSpan P,s) = Comput P,s,k
let P be the Instructions of S -valued ManySortedSet of NAT ; :: thesis: for s being State of S
for k being Element of NAT st CurInstr P,(Comput P,s,k) = halt S holds
Comput P,s,(LifeSpan P,s) = Comput P,s,k
let s be State of S; :: thesis: for k being Element of NAT st CurInstr P,(Comput P,s,k) = halt S holds
Comput P,s,(LifeSpan P,s) = Comput P,s,k
let k be Element of NAT ; :: thesis: ( CurInstr P,(Comput P,s,k) = halt S implies Comput P,s,(LifeSpan P,s) = Comput P,s,k )
assume A1: CurInstr P,(Comput P,s,k) = halt S ; :: thesis: Comput P,s,(LifeSpan P,s) = Comput P,s,k
dom P = NAT by PARTFUN1:def 4;
then X: IC (Comput P,s,k) in dom P ;
A2: P halts_on s by Def20, X, A1;
set Ls = LifeSpan P,s;
A3: CurInstr P,(Comput P,s,(LifeSpan P,s)) = halt S by A2, Def46;
LifeSpan P,s <= k by A1, A2, Def46;
hence Comput P,s,(LifeSpan P,s) = Comput P,s,k by A3, Th52; :: thesis: verum