let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for p being PartState of S holds DataPart (Initialize p) = DataPart p
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over 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 Th20
.= DataPart p ; :: thesis: verum