mirror of https://github.com/nmvdw/HITs-Examples
Split the development into different directories
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Require Export HoTT HitTactics.
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Require Export representations.definition.
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From fsets Require Export
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monad
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extensionality
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properties
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properties_decidable.
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-R ../prelude ""
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-R ../prelude ""
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lattice.v
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lattice.v
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disjunction.v
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disjunction.v
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bad.v
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representations/bad.v
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definition.v
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representations/definition.v
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operations.v
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fsets/operations.v
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properties.v
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fsets/properties.v
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operations_decidable.v
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fsets/operations_decidable.v
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extensionality.v
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fsets/extensionality.v
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properties_decidable.v
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fsets/properties_decidable.v
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monad.v
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fsets/monad.v
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cons_repr.v
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FSets.v
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lists.v
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representations/cons_repr.v
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enumerated.v
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implementations/lists.v
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variations/enumerated.v
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#empty_set.v
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#empty_set.v
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#ordered.v
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#ordered.v
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(** Extensionality of the FSets *)
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(** Extensionality of the FSets *)
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Import definition operations properties.
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From representations Require Import definition.
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From fsets Require Import operations properties.
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Section ext.
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Section ext.
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Context {A : Type}.
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Context {A : Type}.
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(* [FSet] is a (strong and stable) finite powerset monad *)
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(* [FSet] is a (strong and stable) finite powerset monad *)
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Export definition properties.
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Require Export representations.definition fsets.properties.
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Definition ffmap {A B : Type} : (A -> B) -> FSet A -> FSet B.
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Definition ffmap {A B : Type} : (A -> B) -> FSet A -> FSet B.
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Proof.
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Proof.
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(* Operations on the [FSet A] for an arbitrary [A] *)
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(* Operations on the [FSet A] for an arbitrary [A] *)
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Import definition disjunction lattice.
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Require Import representations.definition disjunction lattice.
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Section operations.
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Section operations.
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Context {A : Type}.
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Context {A : Type}.
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(* Operations on [FSet A] when [A] has decidable equality *)
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(* Operations on [FSet A] when [A] has decidable equality *)
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Export definition operations.
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Require Export representations.definition fsets.operations.
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Section decidable_A.
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Section decidable_A.
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Context {A : Type}.
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Context {A : Type}.
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Export definition operations disjunction.
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Require Export representations.definition disjunction fsets.operations.
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(* Lemmas relating operations to the membership predicate *)
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(* Lemmas relating operations to the membership predicate *)
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Section operations_isIn.
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Section operations_isIn.
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(* Properties of [FSet A] where [A] has decidable equality *)
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(* Properties of [FSet A] where [A] has decidable equality *)
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Export properties extensionality lattice operations_decidable.
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From fsets Require Export properties extensionality operations_decidable.
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Require Export lattice.
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(* Lemmas relating operations to the membership predicate *)
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(* Lemmas relating operations to the membership predicate *)
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Section operations_isIn.
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Section operations_isIn.
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Import cons_repr operations_decidable properties_decidable definition.
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Require Import representations.cons_repr FSets.
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Section Operations.
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Section Operations.
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Variable A : Type.
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Variable A : Type.
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Require Import HoTT HitTactics.
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Require Import HoTT HitTactics.
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Require Import definition operations_decidable properties_decidable.
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Require Import representations.definition.
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From fsets Require Import operations_decidable properties_decidable.
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Module Export FSetC.
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Module Export FSetC.
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