Section 6.12 量词辖域的扩张
设公式A中含x, 公式B中不出现x
Objectives: 全称量词辖域的扩张
- \(\displaystyle \forall x A(x) \vee B \Iff \forall x(A(x) \vee B) \)
- \(\displaystyle \forall x A(x) \wedge B \Iff \forall x(A(x) \wedge B) \)
Objectives: 存在量词辖域的扩张
- \(\displaystyle \exists x A(x) \vee B \Iff \exists x (A(x) \vee B) \)
- \(\displaystyle \exists x A(x) \wedge B \Iff \exists x (A(x) \wedge B) \)