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Removed tauto_hooo_rev_imply #667

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merged 1 commit into from Dec 19, 2022
Merged

Removed tauto_hooo_rev_imply #667

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21 changes: 8 additions & 13 deletions src/hooo.rs
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Expand Up @@ -127,8 +127,9 @@ pub fn pow_refl<A: Prop>(x: A) -> A {x}

/// `a^b => (¬b)^(¬a)`.
pub fn pow_modus_tollens<A: Prop, B: Prop>(x: Pow<A, B>) -> Pow<Not<B>, Not<A>> {
pow_transitivity(pow_transitivity(pow_to_imply, imply::modus_tollens),
tauto_imply_to_pow(tauto_hooo_rev_imply(pow_to_imply_lift(tauto_pow_imply))))(x)
// pow_transitivity(pow_transitivity(pow_to_imply, imply::modus_tollens),
// tauto_imply_to_pow(tauto_hooo_rev_imply(pow_to_imply_lift(tauto_pow_imply))))(x)
unimplemented!()
}

/// `a^b ⋀ (a == c)^true => c^b`.
Expand Down Expand Up @@ -267,10 +268,11 @@ fn pow<A: Prop, B: Prop>() -> Pow<A, B>

/// `(¬(a^b))^true => (¬a)^b`.
pub fn tauto_hooo_rev_not<A: Prop, B: Prop>(x: Tauto<Not<Pow<A, B>>>) -> Pow<Not<A>, B> {
fn f<A: Prop, B: Prop>(x: Not<Pow<A, B>>) -> Imply<Pow<A, B>, Para<B>> {
imply::transitivity(x, imply::absurd())
}
tauto_hooo_rev_imply(pow_transitivity(x, f))
// fn f<A: Prop, B: Prop>(x: Not<Pow<A, B>>) -> Imply<Pow<A, B>, Para<B>> {
// imply::transitivity(x, imply::absurd())
// }
// tauto_hooo_rev_imply(pow_transitivity(x, f))
unimplemented!()
}

/// `¬(a^b) => (¬a)^b`.
Expand Down Expand Up @@ -482,13 +484,6 @@ pub fn tauto_hooo_imply<A: Prop, B: Prop, C: Prop>(
unimplemented!()
}

/// `(a^c => b^c)^true => (a => b)^c`.
pub fn tauto_hooo_rev_imply<A: Prop, B: Prop, C: Prop>(
x: Tauto<Imply<Pow<A, C>, Pow<B, C>>>
) -> Pow<Imply<A, B>, C> {
unimplemented!()
}

/// `(a => b)^c => (a^c => b^c)`.
pub fn hooo_imply<A: Prop, B: Prop, C: Prop>(
x: Pow<Imply<A, B>, C>
Expand Down