diff --git a/src/test/ui/higher-rank-trait-bounds/normalize-under-binder/issue-56556.rs b/src/test/ui/higher-rank-trait-bounds/normalize-under-binder/issue-56556.rs
new file mode 100644
index 00000000000..768d1c36619
--- /dev/null
+++ b/src/test/ui/higher-rank-trait-bounds/normalize-under-binder/issue-56556.rs
@@ -0,0 +1,13 @@
+// check-pass
+
+fn foo<T>(t: T) -> usize
+where
+    for<'a> &'a T: IntoIterator,
+    for<'a> <&'a T as IntoIterator>::IntoIter: ExactSizeIterator,
+{
+    t.into_iter().len()
+}
+
+fn main() {
+    foo::<Vec<u32>>(vec![]);
+}
diff --git a/src/test/ui/higher-rank-trait-bounds/normalize-under-binder/issue-76956.rs b/src/test/ui/higher-rank-trait-bounds/normalize-under-binder/issue-76956.rs
new file mode 100644
index 00000000000..583470080a2
--- /dev/null
+++ b/src/test/ui/higher-rank-trait-bounds/normalize-under-binder/issue-76956.rs
@@ -0,0 +1,15 @@
+// check-pass
+
+use std::ops::Deref;
+
+struct Data {
+    boxed: Box<&'static i32>
+}
+
+impl Data {
+    fn use_data(&self, user: impl for <'a> FnOnce(<Box<&'a i32> as Deref>::Target)) {
+        user(*self.boxed)
+    }
+}
+
+fn main() {}