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 p halts_on s holds

Result (p,s) = 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 p halts_on s holds

Result (p,s) = 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 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 Def15;

consider m being Nat such that

A3: Result (p,s) = Comput (p,s,m) and

A4: CurInstr (p,(Result (p,s))) = halt S by A1, Def9;

LifeSpan (p,s) <= m by A1, A3, A4, Def15;

hence Result (p,s) = Comput (p,s,(LifeSpan (p,s))) by A2, A3, Th5; :: thesis: verum

for p being NAT -defined the InstructionsF of b

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 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 p halts_on s holds

Result (p,s) = 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 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 Def15;

consider m being Nat such that

A3: Result (p,s) = Comput (p,s,m) and

A4: CurInstr (p,(Result (p,s))) = halt S by A1, Def9;

LifeSpan (p,s) <= m by A1, A3, A4, Def15;

hence Result (p,s) = Comput (p,s,(LifeSpan (p,s))) by A2, A3, Th5; :: thesis: verum