let N be non empty with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for P being Instruction-Sequence of S
for s being State of S
for k being 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 with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S
for s being State of S
for k being Nat st CurInstr (P,(Comput (P,s,k))) = halt S holds
Comput (P,s,(LifeSpan (P,s))) = Comput (P,s,k)

let P be Instruction-Sequence of S; :: thesis: for s being State of S
for k being 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 Nat st CurInstr (P,(Comput (P,s,k))) = halt S holds
Comput (P,s,(LifeSpan (P,s))) = Comput (P,s,k)

let k be 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)
A2: dom P = NAT by PARTFUN1:def 2;
A3: P halts_on s by A2, A1;
set Ls = LifeSpan (P,s);
A4: CurInstr (P,(Comput (P,s,(LifeSpan (P,s))))) = halt S by ;
LifeSpan (P,s) <= k by ;
hence Comput (P,s,(LifeSpan (P,s))) = Comput (P,s,k) by ; :: thesis: verum