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 NAT -defined the Instructions of b₁ -valued Function
for s being State of S st p halts_on s holds
Result (p,s) = Comput (p,s,(LifeSpan (p,s)))
let S be non empty IC-Ins-separated halting AMI-Struct of N; :: thesis: for p being NAT -defined the Instructions of S -valued Function
for s being State of S st p halts_on s holds
Result (p,s) = Comput (p,s,(LifeSpan (p,s)))
let p be NAT -defined the Instructions of S -valued Function; :: thesis: for s being State of S st p halts_on s holds
Result (p,s) = Comput (p,s,(LifeSpan (p,s)))
let s be State of S; :: thesis: ( p halts_on s implies Result (p,s) = Comput (p,s,(LifeSpan (p,s))) )
assume A1: p halts_on s ; :: thesis: Result (p,s) = Comput (p,s,(LifeSpan (p,s)))
then A2: CurInstr (p,(Comput (p,s,(LifeSpan (p,s))))) = halt S by Def14;
consider m being Element of NAT such that
A3: Result (p,s) = Comput (p,s,m) and
A4: CurInstr (p,(Result (p,s))) = halt S by A1, Def8;
LifeSpan (p,s) <= m by A1, A3, A4, Def14;
hence Result (p,s) = Comput (p,s,(LifeSpan (p,s))) by A2, A3, Th6; :: thesis: verum