let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for p being FinPartState of S
for k being Element of NAT holds DataPart (DecIC (p,k)) = DataPart p
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being FinPartState of S
for k being Element of NAT holds DataPart (DecIC (p,k)) = DataPart p
let p be FinPartState of S; :: thesis: for k being Element of NAT holds DataPart (DecIC (p,k)) = DataPart p
let k be Element of NAT ; :: thesis: DataPart (DecIC (p,k)) = DataPart p
thus DataPart (DecIC (p,k)) = (DataPart p) +* (DataPart (Start-At (((IC p) -' k),S))) by FUNCT_4:75
.= (DataPart p) +* {} by Th30
.= DataPart p by FUNCT_4:22 ; :: thesis: verum