diff --git a/web/examples/ffi.flan b/web/examples/ffi.flan
index d34ca00..6429f95 100644
--- a/web/examples/ffi.flan
+++ b/web/examples/ffi.flan
@@ -1,6 +1,11 @@
 ;; A plain `declare` names a C symbol in a signature Flan can already spell:
 ;; no aggregate crosses, so no wrapper is generated.
-(declare cos-f64 [x f64] f64 "cos")
+;;
+;; cosh and not cos, because the prelude already declares cos-f64 and a second
+;; declaration of a name is refused with both sites named. That refusal is the
+;; useful half of this example: the prelude is where the common libm calls
+;; live, and a `declare` is how you reach one it does not name.
+(declare cosh-f64 [x f64] f64 "cosh")
 
 (defn main [] ()
-  (print (cos-f64 0.0)) (println ""))
+  (print (cosh-f64 0.0)) (println ""))
diff --git a/web/index.html b/web/index.html
index d8d80e5..8860532 100644
--- a/web/index.html
+++ b/web/index.html
@@ -1418,14 +1418,19 @@ structural rule could tell them apart.</p>
 <p><code>declare</code> names a C symbol in a signature Flan can already spell. Nothing
 is generated; a Flan string crosses as ptr+len, exactly as it is stored.</p>
 
-<pre><code>(declare cos-f64 [x f64] f64 "cos")
+<pre><code>(declare cosh-f64 [x f64] f64 "cosh")
 
 (defn main [] ()
-  (print (cos-f64 0.0)) (println ""))</code></pre>
+  (print (cosh-f64 0.0)) (println ""))</code></pre>
 
 <pre><code class="sh">1</code></pre>
 
-<p>That is 1.0, printed by the same rule as before.</p>
+<p>That is 1.0, printed by the same rule as before. It is <code>cosh</code> and not
+<code>cos</code> because <a href="#prelude">the prelude</a> already declares
+<code>cos-f64</code>, and a second declaration of a name is refused with both sites
+named — which is the other half of what this example shows. The prelude is where the
+common libm calls live; a <code>declare</code> is how you reach one it does not
+name.</p>
 
 <p><code>declare-c</code> names the C library's own function in the C library's own
 signature, and the compiler writes the wrapper. This is what raylib's package is made