let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite halting steady-programmed AMI-Struct of N
for P being the Instructions of b₁ -valued ManySortedSet of NAT
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 stored-program IC-Ins-separated definite halting steady-programmed AMI-Struct of N; :: thesis: for P being the Instructions of S -valued ManySortedSet of NAT
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 the Instructions of S -valued ManySortedSet of NAT ; :: 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 21;
hence Result P,s = Result P,(Comput P,s,i) by Th57; :: thesis: verum