n-push : {m : Meta} {{_ : M.DataSegment Meta}} (n : ℕ) -> M.CodeSegment Meta Meta
n-push {{mm}} (zero)      = M.cs {{mm}} {{mm}} id
n-push {m} {{mm}} (suc n) = M.cs {{mm}} {{mm}} (\m -> M.exec {{mm}} {{mm}} (n-push {m} {{mm}} n) (pushOnce m))

n-pop : {m : Meta} {{_ : M.DataSegment Meta}} (n : ℕ) -> M.CodeSegment Meta Meta
n-pop {{mm}} (zero)      = M.cs {{mm}} {{mm}} id
n-pop {m} {{mm}} (suc n) = M.cs {{mm}} {{mm}} (\m -> M.exec {{mm}} {{mm}} (n-pop {m} {{mm}} n) (popOnce m))

pop-n-push-type : ℕ -> ℕ -> ℕ -> SingleLinkedStack ℕ -> Set₁
pop-n-push-type n cn ce s = M.exec (M.csComp {meta} (M.cs popOnce) (n-push {meta} (suc n))) meta
                         ≡ M.exec (n-push {meta} n) meta
  where
    meta = id-meta cn ce s