let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for k being natural number
for l1, l2 being Element of NAT st Start-At (l1,S) = Start-At (l2,S) holds
Start-At ((l1 -' k),S) = Start-At ((l2 -' k),S)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for k being natural number
for l1, l2 being Element of NAT st Start-At (l1,S) = Start-At (l2,S) holds
Start-At ((l1 -' k),S) = Start-At ((l2 -' k),S)
let k be natural number ; :: thesis: for l1, l2 being Element of NAT st Start-At (l1,S) = Start-At (l2,S) holds
Start-At ((l1 -' k),S) = Start-At ((l2 -' k),S)
let l1, l2 be Element of NAT ; :: thesis: ( Start-At (l1,S) = Start-At (l2,S) implies Start-At ((l1 -' k),S) = Start-At ((l2 -' k),S) )
assume Start-At (l1,S) = Start-At (l2,S) ; :: thesis: Start-At ((l1 -' k),S) = Start-At ((l2 -' k),S)
then {[(IC S),l1]} = Start-At (l2,S) by FUNCT_4:87
.= {[(IC S),l2]} by FUNCT_4:87 ;
then [(IC S),l1] = [(IC S),l2] by ZFMISC_1:6;
hence Start-At ((l1 -' k),S) = Start-At ((l2 -' k),S) by ZFMISC_1:33; :: thesis: verum