Add basic properties of ≤

2 files changed, 22 insertions, 1 deletions

diff --git a/src/Cfe/Language/Base.agda b/src/Cfe/Language/Base.agda
index eeea11d..2e77b11 100644
--- a/src/Cfe/Language/Base.agda
+++ b/src/Cfe/Language/Base.agda
@@ -46,4 +46,4 @@ fix : (Language → Language) → Language
 fix f l = ∃[ n ] iterate f n ∅ l
 
 _≤_ : Language → Language → Set (a ⊔ ℓ)
-A ≤ B = ∀ l → A l → B l
+A ≤ B = ∀ {l} → A l → B l
diff --git a/src/Cfe/Language/Properties.agda b/src/Cfe/Language/Properties.agda
new file mode 100644
index 0000000..8d024a8
--- /dev/null
+++ b/src/Cfe/Language/Properties.agda
@@ -0,0 +1,21 @@
+{-# OPTIONS --without-K --safe #-}
+
+open import Relation.Binary
+
+module Cfe.Language.Properties
+  {a ℓ} (setoid : Setoid a ℓ)
+  where
+
+open Setoid setoid renaming (Carrier to A)
+
+open import Cfe.Language setoid
+open import Function
+
+------------------------------------------------------------------------
+-- Properties of _≤_
+
+≤-refl : Reflexive _≤_
+≤-refl = id
+
+≤-trans : Transitive _≤_
+≤-trans A≤B B≤C = B≤C ∘ A≤B