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 Instruction-Sequence of S

for s being State of S

for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S

for s being State of S

for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let P be Instruction-Sequence of S; :: thesis: for s being State of S

for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let s be State of S; :: thesis: for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let k be Nat; :: thesis: ( P . (IC (Comput (P,s,k))) = halt S implies Result (P,s) = Comput (P,s,k) )

A1: dom P = NAT by PARTFUN1:def 2;

assume P . (IC (Comput (P,s,k))) = halt S ; :: thesis: Result (P,s) = Comput (P,s,k)

then A2: CurInstr (P,(Comput (P,s,k))) = halt S by A1, PARTFUN1:def 6;

then P halts_on s by A1;

hence Result (P,s) = Comput (P,s,k) by A2, Def9; :: thesis: verum

for P being Instruction-Sequence of S

for s being State of S

for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S

for s being State of S

for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let P be Instruction-Sequence of S; :: thesis: for s being State of S

for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let s be State of S; :: thesis: for k being Nat st P . (IC (Comput (P,s,k))) = halt S holds

Result (P,s) = Comput (P,s,k)

let k be Nat; :: thesis: ( P . (IC (Comput (P,s,k))) = halt S implies Result (P,s) = Comput (P,s,k) )

A1: dom P = NAT by PARTFUN1:def 2;

assume P . (IC (Comput (P,s,k))) = halt S ; :: thesis: Result (P,s) = Comput (P,s,k)

then A2: CurInstr (P,(Comput (P,s,k))) = halt S by A1, PARTFUN1:def 6;

then P halts_on s by A1;

hence Result (P,s) = Comput (P,s,k) by A2, Def9; :: thesis: verum