let j be Element of NAT ; :: thesis: for N being non empty with_non-empty_elements set
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 b₂ -valued Function
for s being State of S st LifeSpan p,s <= j & p halts_on s holds
Comput p,s,j = Comput p,s,(LifeSpan p,s)
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 LifeSpan p,s <= j & p halts_on s holds
Comput p,s,j = 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 LifeSpan p,s <= j & p halts_on s holds
Comput p,s,j = 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 LifeSpan p,s <= j & p halts_on s holds
Comput p,s,j = Comput p,s,(LifeSpan p,s)
let s be State of S; :: thesis: ( LifeSpan p,s <= j & p halts_on s implies Comput p,s,j = Comput p,s,(LifeSpan p,s) )
assume that
A1: LifeSpan p,s <= j and
A2: p halts_on s ; :: thesis: Comput p,s,j = Comput p,s,(LifeSpan p,s)
CurInstr p,(Comput p,s,(LifeSpan p,s)) = halt S by A2, Def46;
hence Comput p,s,j = Comput p,s,(LifeSpan p,s) by A1, Th52; :: thesis: verum