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@ -215,7 +215,7 @@ example {p q : Prop} (H_pq : p → q) (H_pnq : p → ¬q) : ¬p := by
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exact show False from H_nq H_q
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```
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### Negation Elimination
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### Double Negation Elimination
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One common representation of negation elimination is to remove any double negations.
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That is $\neg \neg P$ becomes $P$.
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@ -261,6 +261,8 @@ example {p: Prop} (H_nnp : ¬¬p) : p := by
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exact show p from False.elim H_false
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```
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Lean has this theorem built-in with `Classical.not_not`.
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## First Order
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Lean is also capable of reasoning over first order logic. In this section, we'll start seeing objects/terms and predicates instead of just propositions.
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@ -498,3 +500,6 @@ inductions as writing out the cases explicitly can be daunting.
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If you catch any mistakes in me converting this post, let me know.
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Otherwise feel free to email me if you have any questions.
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Lastly, I want to give my thanks to James Oswald for helping proofread
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this post and making it better.
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