patrick/agdaproofs
1
0
Fork 0
mirror of https://github.com/Smaug123/agdaproofs synced 2025-10-17 01:18:40 +00:00
Code Issues Packages Projects Releases Wiki Activity

Restructure towards ideals

Browse Source
This commit is contained in:
Smaug123
2019-11-20 21:20:03 +00:00
parent f2f4e867fc
commit b03a5279bc
22 changed files with 417 additions and 296 deletions
Download Patch File Download Diff File Expand all files Collapse all files

21
Setoids/Subset.agda Normal file
View File

@@ -0,0 +1,21 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import LogicalFormulae
open import Sets.EquivalenceRelations
open import Setoids.Setoids
module Setoids.Subset {a b : _} {A : Set a} (S : Setoid {a} {b} A) where
open Setoid S
open Equivalence eq
subset : {c : _} (pred : A → Set c) → Set (a ⊔ b ⊔ c)
subset pred = ({x y : A} → x ∼ y → pred x → pred y)
subsetSetoid : {c : _} {pred : A → Set c} → (subs : subset pred) → Setoid (Sg A pred)
Setoid._∼_ (subsetSetoid subs) (x , predX) (y , predY) = Setoid._∼_ S x y
Equivalence.reflexive (Setoid.eq (subsetSetoid subs)) {a , b} = reflexive
Equivalence.symmetric (Setoid.eq (subsetSetoid subs)) {a , prA} {b , prB} x = symmetric x
Equivalence.transitive (Setoid.eq (subsetSetoid subs)) {a , prA} {b , prB} {c , prC} x y = transitive x y