changes

SubjectReduction/Specification.agda

@@ -37,8 +37,8 @@ data Term : ℕ → Set where
   `Setω_  : ∀ {n} (l : Term n) → Term n
   `Setn_  : ∀ {n} (l : Term n) → Term n
   `Level  : ∀ {n} → Term n
-  `lzero     : ∀ {n} → Term n
-  `lsuc     : ∀ {n} → Term n → Term n
+  `lzero  : ∀ {n} → Term n
+  `lsuc   : ∀ {n} → Term n → Term n
   _`⊔_    : ∀ {n} → Term n → Term n → Term n
 
   -- Extension
@@ -149,10 +149,10 @@ mutual
     val-Level : ∀ {n}
       → Value {n = n} `Level
 
-    val-l : ∀ {n v}
+    val-l : ∀ {n}
       → Value {n = n} (`lzero)
 
-    val-lsuc : ∀ {n v l}
+    val-lsuc : ∀ {n l}
       → Value l
       → Value {n = n} (`lsuc l)
 
@@ -289,7 +289,7 @@ data _↪_ : ∀ {n} → Term n → Term n → Set where
     → e₂ ↪ e₂'
     → `subst t e₁ e₂ ↪ `subst t e₁ e₂'
 
--- Extension:
+-- New
   ξ-⊔₁ : ∀ {n} {t₁ t₁' : Term n} {t₂ : Term n}
     → t₁ ↪ t₁'
     -------------------------------
@@ -300,6 +300,10 @@ data _↪_ : ∀ {n} → Term n → Term n → Set where
     -------------------------------
     → (t₁ `⊔ t₂) ↪ (t₁ `⊔ t₂')
 
+  ξ-lsuc : ∀ {n} {l l' : Term n}
+    → l ↪ l'
+    → `lsuc l ↪ `lsuc l'
+
   ξ-Setn : ∀ {n} {l l' : Term n}
     → l ↪ l'
     → `Setn l ↪ `Setn l'
@@ -467,3 +471,4 @@ data _⊢_⦂_ : ∀ {n} → Context n → Term n → Term n → Set where
 
 cong₃ : ∀ {A B C D : Set} (f : A → B → C → D) {x y u v a b} → x ≡ y → u ≡ v → a ≡ b → f x u a ≡ f y v b
 cong₃ f refl refl refl = refl
+