let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite halting steady-programmed 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 stored-program IC-Ins-separated definite halting steady-programmed 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 Def46;
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, Def22;
LifeSpan p,s <= m by A1, A3, A4, Def46;
hence Result p,s = Comput p,s,(LifeSpan p,s) by A2, A3, Th52; :: thesis: verum