Logic P→的形式证明；Q≡¬；P∨；惠誉Q

我正试图为'p'构造一个正式的证明→ Q≡ P∨ 惠誉的问题。我知道这是真的，但我如何证明呢？

我终于设法解决了这个问题：

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实际上相当直截了当

我终于设法解决了这个问题：

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实际上相当直接

给定p⇒ q、 使用惠誉系统证明∨ 问题

1.  p => q            Premise
2.    ~(~p | q)       Assumption
3.      ~p            Assumption
4.      ~p | q        Or Introduction: 3
5.    ~p => ~p | q    Implication Introduction: 3, 4
6.     ~p             Assumption
7.     ~(~p | q)      Reiteration: 2
8.    ~p => ~(~p | q) Implication Introduction: 6, 7
9.    ~~p             Negation Introduction: 5, 8
10.   p               Negation Elimination: 9
11.   q               Implication Elimination: 1, 10
12.   ~p | q          Or Introduction: 11
13. ~(~p | q) => ~p | q        Implication Introduction: 2, 12
14.  ~(~p | q)                 Assumption
15. ~(~p | q) => ~(~p | q)     Implication Introduction: 14, 14
16. ~~(~p | q)                 Negation Introduction: 13, 15
17. ~p | q                     Negation Elimination: 16

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目标~p| q完成

给定p⇒ q、 使用惠誉系统证明∨ 问题

1.  p => q            Premise
2.    ~(~p | q)       Assumption
3.      ~p            Assumption
4.      ~p | q        Or Introduction: 3
5.    ~p => ~p | q    Implication Introduction: 3, 4
6.     ~p             Assumption
7.     ~(~p | q)      Reiteration: 2
8.    ~p => ~(~p | q) Implication Introduction: 6, 7
9.    ~~p             Negation Introduction: 5, 8
10.   p               Negation Elimination: 9
11.   q               Implication Elimination: 1, 10
12.   ~p | q          Or Introduction: 11
13. ~(~p | q) => ~p | q        Implication Introduction: 2, 12
14.  ~(~p | q)                 Assumption
15. ~(~p | q) => ~(~p | q)     Implication Introduction: 14, 14
16. ~~(~p | q)                 Negation Introduction: 13, 15
17. ~p | q                     Negation Elimination: 16

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<>目标~P q q完成< /p>你会考虑一个真值表作为证据吗？不，我在FITCH中寻找一个正式的证明。你会考虑一个真值表作为证据吗？不，我在FITCH中寻找一个正式的证据。