怎样证明：FD的推理规则.A8：{X→Y,W→Z}|=X∪（W-Y）→YZ通用一致性定理

Question

怎样证明：FD的推理规则.A8：{X→Y,W→Z} |=X∪（W-Y）→YZ【通用一致性定理】

Answer 1

Solution:
1.X→Y (given)
2.W→Z (given)
3.X→Y∩W (by joint dependence and 1)
4.W-Y→W-Y (self-determination)
5.X∪(W-Y)→(Y∩W)∪(W-Y) =W
(by composition,3,4)
6.X∪(W-Y)→W (simplifying 5)
7.X∪(W-Y)→Z (by transitivity,6,2)
8.X∪(W-Y)→Y∪Z (by composition,1,7)