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
for k being Nat holds DataPart (DecIC (p,k)) = 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
for k being Nat holds DataPart (DecIC (p,k)) = DataPart p
let p be PartState of S; :: thesis: for k being Nat holds DataPart (DecIC (p,k)) = DataPart p
let k be Nat; :: thesis: DataPart (DecIC (p,k)) = DataPart p
thus DataPart (DecIC (p,k)) = (DataPart p) +* (DataPart (Start-At (((IC p) -' k),S))) by FUNCT_4:71
.= (DataPart p) +* {} by Th20
.= DataPart p ; :: thesis: verum