let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite halting AMI-Struct of N
for P being the Instructions of b₁ -valued ManySortedSet of NAT
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 stored-program IC-Ins-separated definite halting AMI-Struct of N; :: thesis: for P being the Instructions of S -valued ManySortedSet of NAT
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 the Instructions of S -valued ManySortedSet of NAT ; :: 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) )
D: dom P = NAT by PARTFUN1:def 4;
assume P . (IC (Comput (P,s,k))) = halt S ; :: thesis: Result (P,s) = Comput (P,s,k)
then A1: CurInstr (P,(Comput (P,s,k))) = halt S by D, PARTFUN1:def 8;
then P halts_on s by Def20, D;
hence Result (P,s) = Comput (P,s,k) by A1, Def22; :: thesis: verum