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Remove HOOO axiom by not[not] <=> not #476

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bvssvni opened this issue Oct 5, 2022 · 2 comments · Fixed by #480
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Remove HOOO axiom by not[not] <=> not #476

bvssvni opened this issue Oct 5, 2022 · 2 comments · Fixed by #480
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bvssvni commented Oct 5, 2022

Currently, one can prove the following:

pub fn proof<A: Prop>() -> False {
    let a: Pow<A, False> = fa();
    let b: Pow<Not<A>, False> = fa();
    hooo_not()(b)(a)
}
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bvssvni commented Oct 5, 2022

It seems sufficient to remove hooo::hooo_not.

@bvssvni bvssvni self-assigned this Oct 5, 2022
bvssvni added a commit to bvssvni/prop that referenced this issue Oct 5, 2022
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Removed hooo_not
0b039f6 
Closes advancedresearch#476

- Made `nnpos_to_nnpara_para` unsafe
- Added `hooo::decide`
- Added `hooo::tauto_decide`
- Added `hooo::para_decide`
- Removed `hooo::pow_not_double_up`
- Removed `hooo::hooo_not`
- Fixed proofs
@bvssvni bvssvni mentioned this issue Oct 5, 2022
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bvssvni commented Dec 19, 2022

This also implies that tauto_hooo_not is invalid, since tauto_hooo_not implies hooo_not.

@bvssvni bvssvni mentioned this issue Dec 19, 2022
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Removed hooo_not bvssvni/prop
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