let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated halting with_explicit_jumps AMI-Struct over N
for I being IC-relocable Instruction of S
for k being Nat
for s being State of S holds (IC (Exec (I,s))) + k = IC (Exec ((IncAddr (I,k)),(IncIC (s,k))))
let S be non empty with_non-empty_values IC-Ins-separated halting with_explicit_jumps AMI-Struct over N; :: thesis: for I being IC-relocable Instruction of S
for k being Nat
for s being State of S holds (IC (Exec (I,s))) + k = IC (Exec ((IncAddr (I,k)),(IncIC (s,k))))
let I be IC-relocable Instruction of S; :: thesis: for k being Nat
for s being State of S holds (IC (Exec (I,s))) + k = IC (Exec ((IncAddr (I,k)),(IncIC (s,k))))
let k be Nat; :: thesis: for s being State of S holds (IC (Exec (I,s))) + k = IC (Exec ((IncAddr (I,k)),(IncIC (s,k))))
let s be State of S; :: thesis: (IC (Exec (I,s))) + k = IC (Exec ((IncAddr (I,k)),(IncIC (s,k))))
A1: k + 0 = k ;
thus (IC (Exec (I,s))) + k = (IC (Exec ((IncAddr (I,0)),s))) + k by COMPOS_0:3
.= IC (Exec ((IncAddr (I,k)),(IncIC (s,k)))) by Def3, A1 ; :: thesis: verum