drop the Function.Equality requirement from GetTypes

We never used the equality property. Thus a simple function is
sufficient here. We always fulfilled the property using ≡-to-Π anyway.

1 files changed, 5 insertions, 7 deletions

diff --git a/FreeTheorems.agda b/FreeTheorems.agda
index 08bbe88..25759e0 100644
--- a/FreeTheorems.agda
+++ b/FreeTheorems.agda
@@ -5,9 +5,7 @@ open import Data.Nat using (ℕ)
 open import Data.List using (List ; map)
 open import Data.Vec using (Vec) renaming (map to mapV)
 open import Function using (_∘_)
-open import Function.Equality using (_⟶_ ; _⟨$⟩_)
-open import Relation.Binary.PropositionalEquality using (_≗_ ; cong) renaming (setoid to EqSetoid)
-open import Relation.Binary using (Setoid)
+open import Relation.Binary.PropositionalEquality using (_≗_)
 
 import GetTypes
 
@@ -36,13 +34,13 @@ module VecVec where
   assume-get {getlen} get = record { getlen = getlen; get = get; free-theorem = free-theorem get }
 
 module PartialVecVec where
-  get-type : {I : Setoid ℓ₀ ℓ₀} → (I ⟶ EqSetoid ℕ) → (I ⟶ EqSetoid ℕ) → Set₁
-  get-type {I} gl₁ gl₂ = {A : Set} {i : Setoid.Carrier I} → Vec A (gl₁ ⟨$⟩ i) → Vec A (gl₂ ⟨$⟩ i)
+  get-type : {I : Set} → (I → ℕ) → (I → ℕ) → Set₁
+  get-type {I} gl₁ gl₂ = {A : Set} {i : I} → Vec A (gl₁ i) → Vec A (gl₂ i)
 
   open GetTypes.PartialVecVec public
 
   postulate
-    free-theorem : {I : Setoid ℓ₀ ℓ₀} → (gl₁ : I ⟶ EqSetoid ℕ) → (gl₂ : I ⟶ EqSetoid ℕ) (get : get-type gl₁ gl₂)  → {α β : Set} → (f : α → β) → {i : Setoid.Carrier I} → get {_} {i} ∘ mapV f ≗ mapV f ∘ get
+    free-theorem : {I : Set} → (gl₁ : I → ℕ) → (gl₂ : I → ℕ) (get : get-type gl₁ gl₂)  → {α β : Set} → (f : α → β) → {i : I} → get {_} {i} ∘ mapV f ≗ mapV f ∘ get
 
-  assume-get : {I : Setoid ℓ₀ ℓ₀} → (gl₁ : I ⟶ EqSetoid ℕ) → (gl₂ : I ⟶ EqSetoid ℕ) (get : get-type gl₁ gl₂) → Get
+  assume-get : {I : Set} → (gl₁ : I → ℕ) → (gl₂ : I → ℕ) (get : get-type gl₁ gl₂) → Get
   assume-get {I} gl₁ gl₂ get = record { I = I; gl₁ = gl₁; gl₂ = gl₂; get = get; free-theorem = free-theorem gl₁ gl₂ get }