Struct prop::True

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pub struct True;

Expand description

Logical true.

Trait Implementations

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impl Clone for True

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fn clone(&self) -> True

Returns a copy of the value. Read more

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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more

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impl Decidable for True

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fn decide() -> ExcM<True>

Get excluded middle rule.

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impl<A: Prop> HomotopyEquality<A> for True

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fn refl() -> Self

hom_eq(n, a, a).

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impl<A: Prop, B: Prop> HomotopyEquivalence<A, B> for True

type N = Z

The associated homotopy level.

type Rel<A2: Prop, B2: Prop> = True

Relation constructor.

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fn transitivity<C: Prop>(self, _: True) -> True

hom_eq(n, a, b) ⋀ hom_eq(n, b, c) => hom_eq(n, a, c).

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fn symmetry(self) -> True

hom_eq(n, a, b) => hom_eq(n, b, a).

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fn cast<A2: Prop, B2: Prop>(_: True) -> True

Cast to self.

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fn cast_lift<A2: Prop, B2: Prop>(self) -> True

Cast to other.

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impl<A: Prop, B: Prop> HomotopyLevel0<A, B> for True

type H0 = True

A type such that it proves homotopy level 0.

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fn h0<X: LProp>(_ty_x: Ty<X, Self>) -> HomEq<Z, True, X>

Homotopy level 0.

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impl Copy for True

Auto Trait Implementations

impl RefUnwindSafe for True

impl Send for True

impl Sync for True

impl Unpin for True

impl UnwindSafe for True

Blanket Implementations

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impl<T> Any for Twhere
T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more

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impl<T> Existential for Twhere
T: Decidable,

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fn e(
) -> Either<Rc<dyn Fn(Rc<dyn Fn(T) + 'static>) + 'static>, Rc<dyn Fn(T) + 'static>>

Get existential rule.

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impl<T> From<T> for T

const: unstable · source

fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into for Twhere
U: From<T>,

const: unstable · source

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> Prop for Twhere
T: 'static + Clone,

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fn double_neg(self) -> Dneg<Self>

Get double negation rule from proof.

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fn map_any<T>(self) -> Imply<T, Self>

Maps anything into itself.

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fn nnexcm() -> Not<Not<ExcM<Self>>>

Double negated excluded middle.

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impl<T> ToOwned for Twhere
T: Clone,

type Owned = T

The resulting type after obtaining ownership.

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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more

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impl<T, U> TryFrom for Twhere
U: Into<T>,

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

fn try_from(value: U) -> Result<T, <T as TryFrom>::Error>

Performs the conversion.

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impl<T, U> TryInto for Twhere
U: TryFrom<T>,

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

fn try_into(self) -> Result<U, >::Error>

Performs the conversion.

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impl<T> DProp for Twhere
T: Decidable,

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impl<T> EProp for Twhere
T: Existential,

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Struct prop::True

Trait Implementations

impl Clone for True

fn clone(&self) -> True

fn clone_from(&mut self, source: &Self)

impl Decidable for True

fn decide() -> ExcM<True>

impl<A: Prop> HomotopyEquality<A> for True

fn refl() -> Self

impl<A: Prop, B: Prop> HomotopyEquivalence<A, B> for True

type N = Z

type Rel<A2: Prop, B2: Prop> = True

fn transitivity<C: Prop>(self, _: True) -> True

fn symmetry(self) -> True

fn cast<A2: Prop, B2: Prop>(_: True) -> True

fn cast_lift<A2: Prop, B2: Prop>(self) -> True

impl<A: Prop, B: Prop> HomotopyLevel0<A, B> for True

type H0 = True

fn h0<X: LProp>(_ty_x: Ty<X, Self>) -> HomEq<Z, True, X>

impl Copy for True

Auto Trait Implementations

impl RefUnwindSafe for True

impl Send for True

impl Sync for True

impl Unpin for True

impl UnwindSafe for True

Blanket Implementations

impl<T> Any for Twhere T: 'static + ?Sized,

fn type_id(&self) -> TypeId

impl<T> Borrow<T> for Twhere T: ?Sized,

fn borrow(&self) -> &T

impl<T> BorrowMut<T> for Twhere T: ?Sized,

fn borrow_mut(&mut self) -> &mut T

impl<T> Existential for Twhere T: Decidable,

fn e() -> Either<Rc<dyn Fn(Rc<dyn Fn(T) + 'static>) + 'static>, Rc<dyn Fn(T) + 'static>>

impl<T> From<T> for T

fn from(t: T) -> T

impl<T, U> Into<U> for Twhere U: From<T>,

fn into(self) -> U

impl<T> Prop for Twhere T: 'static + Clone,

fn double_neg(self) -> Dneg<Self>

fn map_any<T>(self) -> Imply<T, Self>

fn nnexcm() -> Not<Not<ExcM<Self>>>

impl<T> ToOwned for Twhere T: Clone,

type Owned = T

fn to_owned(&self) -> T

fn clone_into(&self, target: &mut T)

impl<T, U> TryFrom<U> for Twhere U: Into<T>,

type Error = Infallible

fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

type Error = <U as TryFrom<T>>::Error

fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

impl<T> DProp for Twhere T: Decidable,

impl<T> EProp for Twhere T: Existential,

impl<T, U> Lt<S<U>> for Twhere T: Lt<U>,

impl<T> Any for Twhere
T: 'static + ?Sized,

impl<T> Borrow<T> for Twhere
T: ?Sized,

impl<T> BorrowMut<T> for Twhere
T: ?Sized,

impl<T> Existential for Twhere
T: Decidable,

fn e(
) -> Either<Rc<dyn Fn(Rc<dyn Fn(T) + 'static>) + 'static>, Rc<dyn Fn(T) + 'static>>

impl<T, U> Into<U> for Twhere
U: From<T>,

impl<T> Prop for Twhere
T: 'static + Clone,

impl<T> ToOwned for Twhere
T: Clone,

impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

impl<T> DProp for Twhere
T: Decidable,

impl<T> EProp for Twhere
T: Existential,

impl<T, U> Lt<S<U>> for Twhere
T: Lt<U>,