Equivalence Rules (Cont.) 8.The projection operation distributes over the theta join operation as follows: (a)if 0 involves only attributes from L1 L2: Πu,(E,凶gE2)=(Π，(E)凶g(Π，(E2)》 (b)Consider a join E1Ne E2. Let L1 and L2 be sets of attributes from E1 and E2, respectively. Let L3 be attributes of E that are involved in join condition 0, but are not in L1L2,and let L be attributes of E2 that are involved in join condition 0, but are not in L1L2. Πu,(E,凶aE2)=Π，u,(Π4u(E)凶Mg(Π，uL(E2)》 Database System Concepts-6th Edition 1.12 ©Silberschat乜，Korth and SudarshanDatabase System Concepts - 6 1.12 ©Silberschatz, Korth and Sudarshan th Edition Equivalence Rules (Cont.) 8. The projection operation distributes over the theta join operation as follows: (a) if  involves only attributes from L1  L2 : (b) Consider a join E1  E2 . Let L1 and L2 be sets of attributes from E1 and E2 , respectively. Let L3 be attributes of E1 that are involved in join condition , but are not in L1  L2 , and let L4 be attributes of E2 that are involved in join condition , but are not in L1  L2 . ( ) ( ( )) ( ( )) L1L2 E1 E2 = L1 E1  L2 E2 ( ) (( ( )) ( ( ))) L1L2 E1 E2 L1L2 L1L3 E1 L2 L4 E2  =  