let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated halting AMI-Struct of N
for P being Instruction-Sequence of S
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 IC-Ins-separated halting AMI-Struct of N; :: thesis: for P being Instruction-Sequence of S
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 Instruction-Sequence of S; :: 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)
A2: dom P = NAT by PARTFUN1:def 2;
A3: P halts_on s by Def7, A2, A1;
set Ls = LifeSpan (P,s);
A4: CurInstr (P,(Comput (P,s,(LifeSpan (P,s))))) = halt S by A3, Def14;
LifeSpan (P,s) <= k by A1, A3, Def14;
hence Comput (P,s,(LifeSpan (P,s))) = Comput (P,s,k) by A4, Th6; :: thesis: verum