Prove that foldr is monotonic when input lists are pairwise monotonic

This should help prove that "join" is monotonic

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

Utils.agda

@@ -1,5 +1,6 @@
 module Utils where
 
+open import Agda.Primitive using () renaming (_⊔_ to _⊔ℓ_)
 open import Data.Nat using (ℕ; suc)
 open import Data.List using (List; []; _∷_; _++_)
 open import Data.List.Membership.Propositional using (_∈_)
@@ -43,3 +44,9 @@ All-x∈xs (x ∷ xs') = here refl ∷ map there (All-x∈xs xs')
 iterate : ∀ {a} {A : Set a} (n : ℕ) → (f : A → A) → A → A
 iterate 0 _ a = a
 iterate (suc n) f a = f (iterate n f a)
+
+data Pairwise {a} {b} {c} {A : Set a} {B : Set b} (P : A → B → Set c) : List A → List B → Set (a ⊔ℓ b ⊔ℓ c)  where
+    [] : Pairwise P [] []
+    _∷_ : ∀ {x : A} {y : B} {xs : List A} {ys : List B} →
+          P x y → Pairwise P xs ys →
+          Pairwise P (x ∷ xs) (y ∷ ys)