let k be Nat; :: thesis: for N being non empty with_zero set
for S being non empty with_non-empty_values IC-Ins-separated AMI-Struct over N
for P being Instruction-Sequence of S
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_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated AMI-Struct over N
for P being Instruction-Sequence of S
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 with_non-empty_values IC-Ins-separated AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S
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 Instruction-Sequence of S; :: 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)))
A1: dom P = NAT by PARTFUN1:def 2;
thus Comput (P,s,(k + 1)) = Following (P,(Comput (P,s,k))) by Th3
.= Exec ((P . (IC (Comput (P,s,k)))),(Comput (P,s,k))) by ; :: thesis: verum