let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for s being State of S
for l being Element of NAT holds DataPart s = DataPart (s +* (Start-At (l,S)))
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for s being State of S
for l being Element of NAT holds DataPart s = DataPart (s +* (Start-At (l,S)))
let s be State of S; :: thesis: for l being Element of NAT holds DataPart s = DataPart (s +* (Start-At (l,S)))
let l be Element of NAT ; :: thesis: DataPart s = DataPart (s +* (Start-At (l,S)))
thus DataPart s = (DataPart s) +* {}
.= (DataPart s) +* (DataPart (Start-At (l,S))) by Th20
.= DataPart (s +* (Start-At (l,S))) by FUNCT_4:71 ; :: thesis: verum