let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated COM-Struct of N
for p being FinPartState of S
for k being Element of NAT holds DataPart (IncrIC p,k) = DataPart p
let S be non empty IC-Ins-separated COM-Struct of N; :: thesis: for p being FinPartState of S
for k being Element of NAT holds DataPart (IncrIC p,k) = DataPart p
let p be FinPartState of S; :: thesis: for k being Element of NAT holds DataPart (IncrIC p,k) = DataPart p
let k be Element of NAT ; :: thesis: DataPart (IncrIC p,k) = DataPart p
thus DataPart (IncrIC p,k) = (DataPart p) +* (DataPart (Start-At ((IC p) + k),S)) by FUNCT_4:75
.= (DataPart p) +* {} by Th138
.= DataPart p by FUNCT_4:22 ; :: thesis: verum