let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated halting AMI-Struct of N
for P being Instruction-Sequence of S
for s being State of S
for k being Element of NAT st P . (IC (Comput (P,s,k))) = halt S holds
Result (P,s) = Comput (P,s,k)
let S be non empty IC-Ins-separated halting AMI-Struct of N; :: thesis: for P being Instruction-Sequence of S
for s being State of S
for k being Element of 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 Element of 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 Element of NAT st P . (IC (Comput (P,s,k))) = halt S holds
Result (P,s) = Comput (P,s,k)
let k be Element of 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 Def7, A1;
hence Result (P,s) = Comput (P,s,k) by A2, Def8; :: thesis: verum