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 I being NAT -defined PartState of holds NPP (Initialize I) = Start-At (0,S)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for I being NAT -defined PartState of holds NPP (Initialize I) = Start-At (0,S)
let I be NAT -defined PartState of ; :: thesis: NPP (Initialize I) = Start-At (0,S)
IC in dom (Initialize I) by Th141;
hence NPP (Initialize I) = (DataPart (Initialize I)) +* (Start-At ((IC (Initialize I)),S)) by Th74
.= (DataPart I) +* (Start-At ((IC (Initialize I)),S)) by Th80
.= {} +* (Start-At ((IC (Initialize I)),S)) by Th209
.= Start-At ((IC (Initialize I)),S) by FUNCT_4:21
.= Start-At (0,S) by Th142 ;
:: thesis: verum