let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of 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 IC-Ins-separated Mem-Struct of 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) +* {} by FUNCT_4:21
.= (DataPart s) +* (DataPart (Start-At (l,S))) by Th30
.= DataPart (s +* (Start-At (l,S))) by FUNCT_4:71 ; :: thesis: verum