let j be Nat; :: thesis: for N being non empty with_zero set

for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N

for p being NAT -defined the InstructionsF of b_{2} -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_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N

for p being NAT -defined the InstructionsF of b_{1} -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 with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for p being NAT -defined the InstructionsF 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 InstructionsF 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, Def15;

hence Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s))) by A1, Th5; :: thesis: verum

for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N

for p being NAT -defined the InstructionsF of b

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_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N

for p being NAT -defined the InstructionsF of b

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 with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for p being NAT -defined the InstructionsF 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 InstructionsF 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, Def15;

hence Comput (p,s,j) = Comput (p,s,(LifeSpan (p,s))) by A1, Th5; :: thesis: verum