Re: [請益] 邏輯證明
※ 引述《a53530 (Susu)》之銘言：
: 1.(x)(Px≡Qx)
: 2.(x)[Px→(Qx→Rx)]
: 3.(Ｅx)Qx v (Ｅx)Px
: /(Ｅx)Rx v (Ｅx)Sx
: 用→替代horseshoe
: 用v 替代或
: 用^ 替代且
: 用(Ｅx)替代有些x
: 我算了好久算不出來
: 請強者幫忙解答
: 將以1000P幣作為酬謝
我來試試。(有些推論規則的名稱我忘了)
1.(x)(Px≡Qx) Ass
2.(x)[Px→(Qx→Rx)] Ass
3.(Ｅx)Qx v (Ｅx)Px Ass
4. ~(Ex)Px Ass for RAA
5. (Ex)Qx 4, 3. DS.
6. Qa 5. EI
7. Pa≡Qa 1. UI
8. (Pa→Qa) ^ (Qa→Pa) from 7
9. (Qa→Pa) 8 Simp
10. Pa 6, 9. MP
11. (x)~Px from 4
12. ~Pa 11. UI
13. Pa^~Pa 10, 12
14. (Ex)Px 4-13. RAA
15. Pb 14, EI
16. (Pb≡Qb) 1. UI
17. (Pb→Qb)^(Qb→Pb) from 16
18. (Pb→Qb) 17 Simp
19. Qb 15, 18 MP
20. [Pb→(Qb→Rb)] 2. UI
21. (Qb→Rb) 15, 20 MP
22. Rb 19, 21 MP
23. (Ex)Rx 22. EU (note that b was introduced
in 15 by EI, so that's fine)
24. (Ex)Rx v (Ex)Sx 23, Add
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