Rationals (#3)

Fields.agda

@@ -19,6 +19,19 @@ module Fields where
       allInvertible : (a : A) → ((a ∼ Group.identity (Ring.additiveGroup R)) → False) → Sg A (λ t → t * a ∼ 1R)
       nontrivial : (0R ∼ 1R) → False
 
+  record Field' {m n : _} : Set (lsuc m ⊔ lsuc n) where
+    field
+      A : Set m
+      S : Setoid {m} {n} A
+      _+_ : A → A → A
+      _*_ : A → A → A
+      R : Ring S _+_ _*_
+      isField : Field R
+
+  encapsulateField : {m n : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (F : Field R) → Field'
+  encapsulateField {A = A} {S = S} {_+_} {_*_} {R} F = record { A = A ; S = S ; _+_ = _+_ ; _*_ = _*_ ; R = R ; isField = F }
+
+
 {-
   record OrderedField {n} {A : Set n} {R : Ring A} (F : Field R) : Set (lsuc n) where
     open Field F