[Agda] binding variables in rewrite pragma

[Michael Shulman]

I've been playing around with the REWRITE pragma, and I'm getting an
error message that I don't understand:

{-# OPTIONS --rewriting #-}

infix 10 _⟼_
postulate
  _⟼_ : {A : Set} → A → A → Set
{-# BUILTIN REWRITE _⟼_ #-}

data _×_ (A B : Set) : Set where
  _,_ : A → B → A × B
fst : (A B : Set) (s : A × B) → A
fst A B (x , y) = x

postulate
  foo : {A : Set} (B : A → Set) → Set
  foo0 : {A : Set} (B C : A → Set) → foo B
  bar : {A : Set} (B : A → Set) (f : (x : A) → B x) → foo B
  bar-fst : (A : Set) (B C : A → Set) (u : (x : A) → B x × C x)
    → bar B (λ (x : A) → fst (B x) (C x) (u x)) ⟼  foo0 B C
{-# REWRITE bar-fst #-}

This produces the error

"bar-fst  is not a legal rewrite rule, since the following variables
are not bound by the left hand side:  C
when checking the pragma REWRITE bar-fst"

I don't understand why C is not bound by the LHS.  Can anyone explain?