let k be natural number ; :: thesis: for N being non empty with_non-empty_elements set
for S being non empty stored-program IC-Ins-separated definite weakly_standard AMI-Struct of N
for l being Element of NAT holds (l + k,S) -' k,S = l
let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite weakly_standard AMI-Struct of N
for l being Element of NAT holds (l + k,S) -' k,S = l
let S be non empty stored-program IC-Ins-separated definite weakly_standard AMI-Struct of N; :: thesis: for l being Element of NAT holds (l + k,S) -' k,S = l
let l be Element of NAT ; :: thesis: (l + k,S) -' k,S = l
thus (l + k,S) -' k,S = il. S,(((locnum l,S) + k) -' k) by Def13
.= il. S,(locnum l,S) by NAT_D:34
.= l by Def13 ; :: thesis: verum