let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of N
for p being PartState of S holds DataPart (Initialize p) = DataPart p
let S be non empty IC-Ins-separated Mem-Struct of N; :: thesis: for p being PartState of S holds DataPart (Initialize p) = DataPart p
let p be PartState of S; :: thesis: DataPart (Initialize p) = DataPart p
thus DataPart (Initialize p) = (DataPart p) +* (DataPart (Start-At (0,S))) by FUNCT_4:71
.= (DataPart p) +* {} by Th30
.= DataPart p by FUNCT_4:21 ; :: thesis: verum