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Open problem: Prove ¬◇a => ⊥^a constructively or prove it is impossible to prove #458

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bvssvni opened this issue Oct 3, 2022 · 1 comment

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@bvssvni
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bvssvni commented Oct 3, 2022

Currently, the proof ¬◇a => ⊥^a requires a do be decidable, which means it only holds in classical logic. See modal::npos_to_para. This will be available in v0.27.

The problem is whether this is possible to do constructively or not.

This requires proving ¬◇a => ⊥^a constructively or ⊥^((¬◇a => ⊥^a)^⊤) constructively (or similar) in Prop.

@bvssvni
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bvssvni commented Oct 4, 2022

Closed by #469

Conclusion: It is constructive.

@bvssvni bvssvni closed this as completed Oct 4, 2022
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