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Added join-semilattice

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Niels
2017-08-08 13:45:27 +02:00
parent c1dfef3cc1
commit de335c3955
2 changed files with 32 additions and 0 deletions
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9
FiniteSets/fsets/properties.v
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@@ -1,6 +1,7 @@
Require Import HoTT HitTactics. Require Import HoTT HitTactics.
From fsets Require Import operations extensionality. From fsets Require Import operations extensionality.
Require Export representations.definition disjunction. Require Export representations.definition disjunction.
Require Import lattice.
(* Lemmas relating operations to the membership predicate *) (* Lemmas relating operations to the membership predicate *)
Section characterize_isIn. Section characterize_isIn.
@@ -119,6 +120,14 @@ Section properties.
Context {A : Type}. Context {A : Type}.
Context `{Univalence}. Context `{Univalence}.
Instance: bottom(FSet A) := ∅.
Instance: maximum(FSet A) := U.
Global Instance joinsemilattice_fset : JoinSemiLattice (FSet A).
Proof.
split ; toHProp.
Defined.
(** comprehension properties *) (** comprehension properties *)
Lemma comprehension_false Y : comprehension (fun (_ : A) => false) Y = ∅. Lemma comprehension_false Y : comprehension (fun (_ : A) => false) Y = ∅.
Proof. Proof.

23
FiniteSets/lattice.v
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@@ -55,6 +55,29 @@ Arguments NeutralL {_} _ _.
Arguments NeutralR {_} _ _. Arguments NeutralR {_} _ _.
Arguments Absorption {_} _ _. Arguments Absorption {_} _ _.
Section JoinSemiLattice.
Variable A : Type.
Context {max_L : maximum A} {empty_L : bottom A}.
Class JoinSemiLattice :=
{
commutative_max_js :> Commutative max_L ;
associative_max_js :> Associative max_L ;
idempotent_max_js :> Idempotent max_L ;
neutralL_max_js :> NeutralL max_L empty_L ;
neutralR_max_js :> NeutralR max_L empty_L ;
}.
End JoinSemiLattice.
Arguments JoinSemiLattice _ {_} {_}.
Create HintDb joinsemilattice_hints.
Hint Resolve associativity : joinsemilattice_hints.
Hint Resolve commutative : joinsemilattice_hints.
Hint Resolve idempotency : joinsemilattice_hints.
Hint Resolve neutralityL : joinsemilattice_hints.
Hint Resolve neutralityR : joinsemilattice_hints.
Section Lattice. Section Lattice.
Variable A : Type. Variable A : Type.
Context {max_L : maximum A} {min_L : minimum A} {empty_L : bottom A}. Context {max_L : maximum A} {min_L : minimum A} {empty_L : bottom A}.