let N be non empty with_zero set ; for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for F being Instruction-Sequence of S
for s being State of S
for k being Nat st IC (Comput (F,s,k)) <> IC (Comput (F,s,(k + 1))) & F . (IC (Comput (F,s,(k + 1)))) = halt S holds
LifeSpan (F,s) = k + 1
let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; for F being Instruction-Sequence of S
for s being State of S
for k being Nat st IC (Comput (F,s,k)) <> IC (Comput (F,s,(k + 1))) & F . (IC (Comput (F,s,(k + 1)))) = halt S holds
LifeSpan (F,s) = k + 1
let F be Instruction-Sequence of S; for s being State of S
for k being Nat st IC (Comput (F,s,k)) <> IC (Comput (F,s,(k + 1))) & F . (IC (Comput (F,s,(k + 1)))) = halt S holds
LifeSpan (F,s) = k + 1
let s be State of S; for k being Nat st IC (Comput (F,s,k)) <> IC (Comput (F,s,(k + 1))) & F . (IC (Comput (F,s,(k + 1)))) = halt S holds
LifeSpan (F,s) = k + 1
let k be Nat; ( IC (Comput (F,s,k)) <> IC (Comput (F,s,(k + 1))) & F . (IC (Comput (F,s,(k + 1)))) = halt S implies LifeSpan (F,s) = k + 1 )
assume that
A1:
IC (Comput (F,s,k)) <> IC (Comput (F,s,(k + 1)))
and
A2:
F . (IC (Comput (F,s,(k + 1)))) = halt S
; LifeSpan (F,s) = k + 1
A3:
dom F = NAT
by PARTFUN1:def 2;
hence
LifeSpan (F,s) = k + 1
by A2, Th31; verum