Some definitions and adjusted proofs

SubjectReduction/SubstitutionPreservesTyping.agda

@@ -58,7 +58,6 @@ sub-type {a = a} _ = a
   → Γ₁ ⊢ e ⦂ t
   ------------------------
   → Γ₂ ⊢ ren ρ e ⦂ ren ρ t
-⊢ren ⊢ρ ⊢-Set = ⊢-Set
 ⊢ren ⊢ρ (⊢-refl ⊢-e) = ⊢-refl (⊢ren ⊢ρ ⊢-e)
 ⊢ren ⊢ρ (⊢-` x refl) = ⊢-` _ (⊢ρ x)
 ⊢ren ⊢ρ (⊢-≡ ⊢l ⊢r) = ⊢-≡ (⊢ren ⊢ρ ⊢l) (⊢ren ⊢ρ ⊢r)
@@ -76,6 +75,14 @@ sub-type {a = a} _ = a
   = ⊢-≈ (≡→≈ (swap-0↦-extᵣ-fusion ρ (term ⊢u₂) t* ))
         (⊢-subst (⊢ren (⊢extᵣ ⊢ρ) t'⊢t) (⊢ren ⊢ρ ⊢u₁) (⊢ren ⊢ρ ⊢u₂) (⊢ren ⊢ρ ⊢≡) 
           (⊢-≈ (≡→≈ (sym (swap-0↦-extᵣ-fusion ρ (term ⊢u₁) (t*)))) (⊢ren ⊢ρ ⊢t[u₁])))
+-- New
+⊢ren ⊢ρ ⊢-Setn = ⊢-Setn
+⊢ren ⊢ρ ⊢-Setω = ⊢-Setω
+⊢ren ⊢ρ ⊢-lzero = ⊢-lzero
+⊢ren ⊢ρ (⊢-lsuc ⊢e) = ⊢-lsuc (⊢ren ⊢ρ  ⊢e)
+⊢ren ⊢ρ (⊢-⊔ ⊢l ⊢r) = ⊢-⊔ (⊢ren ⊢ρ ⊢l) (⊢ren ⊢ρ ⊢r)
+⊢ren ⊢ρ ⊢-Level = ⊢-Level
+
  
 ⊢wk : ∀ {n} {Γ : Context n} {t : Term n}
   → wk ⦂ Γ ⇒ᵣ (Γ , t)
@@ -99,7 +106,6 @@ _⦂_⇒ₛ_ : ∀ {m n} → Sub m n → Context m → Context n → Set
   → Γ₁ ⊢ e ⦂ t
   ------------------------
   → Γ₂ ⊢ sub σ e ⦂ sub σ t
-⊢sub ⊢σ ⊢-Set = ⊢-Set
 ⊢sub ⊢σ (⊢-` x refl) = ⊢σ x
 ⊢sub ⊢σ (⊢-refl e) = ⊢-refl (⊢sub ⊢σ e)
 ⊢sub {σ = σ} ⊢σ (⊢-· ⊢l ⊢r) = ⊢-≈ (≡→≈ (swap-0↦-extₛ-fusion σ (term ⊢r) (∀-type ⊢l))) (⊢-· (⊢sub ⊢σ ⊢l) (⊢sub ⊢σ ⊢r))
@@ -117,6 +123,13 @@ _⦂_⇒ₛ_ : ∀ {m n} → Sub m n → Context m → Context n → Set
   = ⊢-≈ (≡→≈ (swap-0↦-extₛ-fusion σ (term ⊢u₂) t* ))
         (⊢-subst (⊢sub (⊢extₛ ⊢σ) t'⊢t) (⊢sub ⊢σ ⊢u₁) (⊢sub ⊢σ ⊢u₂) (⊢sub ⊢σ ⊢≡) 
           (⊢-≈ (≡→≈ (sym (swap-0↦-extₛ-fusion σ (term ⊢u₁) (t*)))) (⊢sub ⊢σ ⊢t[u₁])))
+-- New
+⊢sub ⊢σ ⊢-Setn = ⊢-Setn
+⊢sub ⊢σ ⊢-Setω = ⊢-Setω
+⊢sub ⊢σ ⊢-lzero = ⊢-lzero
+⊢sub ⊢σ ⊢-Level = ⊢-Level
+⊢sub ⊢σ (⊢-lsuc ⊢e) = ⊢-lsuc (⊢sub ⊢σ ⊢e)
+⊢sub ⊢σ (⊢-⊔ ⊢l ⊢r) = ⊢-⊔ (⊢sub ⊢σ ⊢l) (⊢sub ⊢σ ⊢r)
 
 ⊢sub₁ : ∀ {n} {Γ : Context n} {e : Term n} {t}
   → Γ ⊢ e ⦂ t