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1. leqSub2 :: forall (x_l :: Nat) (x_h :: Nat) (y_l :: Nat) (y_h :: Nat) . LeqProof x_l x_h -> LeqProof y_l y_h -> LeqProof (x_l - y_h) (x_h - y_l)

   parameterized-utils	Data.Parameterized.NatRepr

   Subtract sides of two inequalities.

2. leqSucc :: forall f (z :: Nat) . f z -> LeqProof z (z + 1)

   parameterized-utils	Data.Parameterized.NatRepr

   No documentation available.

3. leqTrans :: forall (m :: Nat) (n :: Nat) (p :: Nat) . LeqProof m n -> LeqProof n p -> LeqProof m p

   parameterized-utils	Data.Parameterized.NatRepr

   Apply transitivity to LeqProof

4. leqZero :: forall (n :: Nat) . LeqProof 0 n

   parameterized-utils	Data.Parameterized.NatRepr

   Zero is less than or equal to any Nat.

5. testEquality :: forall (a :: k) (b :: k) . TestEquality f => f a -> f b -> Maybe (a :~: b)

   parameterized-utils	Data.Parameterized.NatRepr

   Conditionally prove the equality of a and b.

6. testLeq :: forall (m :: Nat) (n :: Nat) . NatRepr m -> NatRepr n -> Maybe (LeqProof m n)

   parameterized-utils	Data.Parameterized.NatRepr

   x testLeq y checks whether x is less than or equal to y.

7. class TestEquality (f :: k -> Type)

   parameterized-utils	Data.Parameterized.Peano

   This class contains types where you can learn the equality of two types from information contained in terms. The result should be Just Refl if and only if the types applied to f are equal:

   testEquality (x :: f a) (y :: f b) = Just Refl ⟺ a = b
   

   Typically, only singleton types should inhabit this class. In that case type argument equality coincides with term equality:

   testEquality (x :: f a) (y :: f b) = Just Refl ⟺ a = b ⟺ x = y
   

   isJust (testEquality x y) = x == y
   

   Singleton types are not required, however, and so the latter two would-be laws are not in fact valid in general.

8. testEquality :: forall (a :: k) (b :: k) . TestEquality f => f a -> f b -> Maybe (a :~: b)

   parameterized-utils	Data.Parameterized.Peano

   Conditionally prove the equality of a and b.

9. class PolyEq u v

   parameterized-utils	Data.Parameterized.TH.GADT

   A polymorphic equality operator that generalizes TestEquality.

10. polyEq :: PolyEq u v => u -> v -> Bool

    parameterized-utils	Data.Parameterized.TH.GADT

    No documentation available.

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