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 st ex k being Element of NAT st P halts_at IC (Comput (P,s,k)) holds
for i being Element of NAT holds Result (P,s) = Result (P,(Comput (P,s,i)))
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 st ex k being Element of NAT st P halts_at IC (Comput (P,s,k)) holds
for i being Element of NAT holds Result (P,s) = Result (P,(Comput (P,s,i)))
let P be Instruction-Sequence of S; :: thesis: for s being State of S st ex k being Element of NAT st P halts_at IC (Comput (P,s,k)) holds
for i being Element of NAT holds Result (P,s) = Result (P,(Comput (P,s,i)))
let s be State of S; :: thesis: ( ex k being Element of NAT st P halts_at IC (Comput (P,s,k)) implies for i being Element of NAT holds Result (P,s) = Result (P,(Comput (P,s,i))) )
given k being Element of NAT such that A1: P halts_at IC (Comput (P,s,k)) ; :: thesis: for i being Element of NAT holds Result (P,s) = Result (P,(Comput (P,s,i)))
let i be Element of NAT ; :: thesis: Result (P,s) = Result (P,(Comput (P,s,i)))
P . (IC (Comput (P,s,k))) = halt S by A1, COMPOS_1:def 12;
hence Result (P,s) = Result (P,(Comput (P,s,i))) by Th8; :: thesis: verum