let k be Element of NAT ; :: thesis: for N being non empty with_non-empty_elements set
for S being non empty stored-program IC-Ins-separated definite AMI-Struct of N
for P being the Instructions of b₂ -valued ManySortedSet of NAT
for s being State of S holds Comput (P,s,(k + 1)) = Exec ((P . (IC (Comput (P,s,k)))),(Comput (P,s,k)))
let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite AMI-Struct of N
for P being the Instructions of b₁ -valued ManySortedSet of NAT
for s being State of S holds Comput (P,s,(k + 1)) = Exec ((P . (IC (Comput (P,s,k)))),(Comput (P,s,k)))
let S be non empty stored-program IC-Ins-separated definite AMI-Struct of N; :: thesis: for P being the Instructions of S -valued ManySortedSet of NAT
for s being State of S holds Comput (P,s,(k + 1)) = Exec ((P . (IC (Comput (P,s,k)))),(Comput (P,s,k)))
let P be the Instructions of S -valued ManySortedSet of NAT ; :: thesis: for s being State of S holds Comput (P,s,(k + 1)) = Exec ((P . (IC (Comput (P,s,k)))),(Comput (P,s,k)))
let s be State of S; :: thesis: Comput (P,s,(k + 1)) = Exec ((P . (IC (Comput (P,s,k)))),(Comput (P,s,k)))
D: dom P = NAT by PARTFUN1:def 4;
thus Comput (P,s,(k + 1)) = Following (P,(Comput (P,s,k))) by Th14
.= Exec ((P . (IC (Comput (P,s,k)))),(Comput (P,s,k))) by D, PARTFUN1:def 8 ; :: thesis: verum