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January 31, 2025 16:00
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Logic Lemma
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| (* https://math.stackexchange.com/questions/447098/why-peirces-law-implies-law-of-excluded-middle *) | |
| Definition strengthen : | |
| forall P : Prop, | |
| (P \/ ~P -> False) -> ~P | |
| := | |
| fun P H p => | |
| let e : ~P := fun p => H (or_introl p) in | |
| H (or_intror e) | |
| . | |
| Definition relax : | |
| forall P : Prop, | |
| P -> P \/ ~P | |
| := | |
| fun P p => | |
| or_introl p. |
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