diff --git a/library/core/src/convert/mod.rs b/library/core/src/convert/mod.rs
index 799085e9a8307..ff5a4c913b7ed 100644
--- a/library/core/src/convert/mod.rs
+++ b/library/core/src/convert/mod.rs
@@ -532,7 +532,7 @@ pub trait Into<T>: Sized {
 #[rustc_diagnostic_item = "From"]
 #[stable(feature = "rust1", since = "1.0.0")]
 #[rustc_on_unimplemented(on(
-    all(_Self = "&str", T = "std::string::String"),
+    all(_Self = "&str", any(T = "alloc::string::String", T = "std::string::String")),
     note = "to coerce a `{T}` into a `{Self}`, use `&*` as a prefix",
 ))]
 pub trait From<T>: Sized {
diff --git a/library/core/src/iter/traits/iterator.rs b/library/core/src/iter/traits/iterator.rs
index dabfce1447483..988352283084b 100644
--- a/library/core/src/iter/traits/iterator.rs
+++ b/library/core/src/iter/traits/iterator.rs
@@ -26,13 +26,13 @@ fn _assert_is_object_safe(_: &dyn Iterator<Item = ()>) {}
 #[stable(feature = "rust1", since = "1.0.0")]
 #[rustc_on_unimplemented(
     on(
-        _Self = "std::ops::RangeTo<Idx>",
+        any(_Self = "core::ops::RangeTo<Idx>", _Self = "std::ops::RangeTo<Idx>"),
         label = "if you meant to iterate until a value, add a starting value",
         note = "`..end` is a `RangeTo`, which cannot be iterated on; you might have meant to have a \
               bounded `Range`: `0..end`"
     ),
     on(
-        _Self = "std::ops::RangeToInclusive<Idx>",
+        any(_Self = "core::ops::RangeToInclusive<Idx>", _Self = "std::ops::RangeToInclusive<Idx>"),
         label = "if you meant to iterate until a value (including it), add a starting value",
         note = "`..=end` is a `RangeToInclusive`, which cannot be iterated on; you might have meant \
               to have a bounded `RangeInclusive`: `0..=end`"
@@ -43,7 +43,7 @@ fn _assert_is_object_safe(_: &dyn Iterator<Item = ()>) {}
     ),
     on(_Self = "&[]", label = "`{Self}` is not an iterator; try calling `.iter()`"),
     on(
-        _Self = "std::vec::Vec<T, A>",
+        any(_Self = "alloc::vec::Vec<T, A>", _Self = "std::vec::Vec<T, A>"),
         label = "`{Self}` is not an iterator; try calling `.into_iter()` or `.iter()`"
     ),
     on(
@@ -51,7 +51,7 @@ fn _assert_is_object_safe(_: &dyn Iterator<Item = ()>) {}
         label = "`{Self}` is not an iterator; try calling `.chars()` or `.bytes()`"
     ),
     on(
-        _Self = "std::string::String",
+        any(_Self = "alloc::string::String", _Self = "std::string::String"),
         label = "`{Self}` is not an iterator; try calling `.chars()` or `.bytes()`"
     ),
     on(
diff --git a/library/core/src/marker.rs b/library/core/src/marker.rs
index 760e58276fc9f..e251015dd8600 100644
--- a/library/core/src/marker.rs
+++ b/library/core/src/marker.rs
@@ -575,59 +575,59 @@ impl<T: ?Sized> Copy for &T {}
 #[lang = "sync"]
 #[rustc_on_unimplemented(
     on(
-        _Self = "std::cell::OnceCell<T>",
+        any(_Self = "core::cell:OnceCell<T>", _Self = "std::cell::OnceCell<T>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::OnceLock` instead"
     ),
     on(
-        _Self = "std::cell::Cell<u8>",
+        any(_Self = "core::cell::Cell<u8>", _Self = "std::cell::Cell<u8>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicU8` instead",
     ),
     on(
-        _Self = "std::cell::Cell<u16>",
+        any(_Self = "core::cell::Cell<u16>", _Self = "std::cell::Cell<u16>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicU16` instead",
     ),
     on(
-        _Self = "std::cell::Cell<u32>",
+        any(_Self = "core::cell::Cell<u32>", _Self = "std::cell::Cell<u32>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicU32` instead",
     ),
     on(
-        _Self = "std::cell::Cell<u64>",
+        any(_Self = "core::cell::Cell<u64>", _Self = "std::cell::Cell<u64>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicU64` instead",
     ),
     on(
-        _Self = "std::cell::Cell<usize>",
+        any(_Self = "core::cell::Cell<usize>", _Self = "std::cell::Cell<usize>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicUsize` instead",
     ),
     on(
-        _Self = "std::cell::Cell<i8>",
+        any(_Self = "core::cell::Cell<i8>", _Self = "std::cell::Cell<i8>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicI8` instead",
     ),
     on(
-        _Self = "std::cell::Cell<i16>",
+        any(_Self = "core::cell::Cell<i16>", _Self = "std::cell::Cell<i16>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicI16` instead",
     ),
     on(
-        _Self = "std::cell::Cell<i32>",
+        any(_Self = "core::cell::Cell<i32>", _Self = "std::cell::Cell<i32>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicI32` instead",
     ),
     on(
-        _Self = "std::cell::Cell<i64>",
+        any(_Self = "core::cell::Cell<i64>", _Self = "std::cell::Cell<i64>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicI64` instead",
     ),
     on(
-        _Self = "std::cell::Cell<isize>",
+        any(_Self = "core::cell::Cell<isize>", _Self = "std::cell::Cell<isize>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicIsize` instead",
     ),
     on(
-        _Self = "std::cell::Cell<bool>",
+        any(_Self = "core::cell::Cell<bool>", _Self = "std::cell::Cell<bool>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` or `std::sync::atomic::AtomicBool` instead",
     ),
     on(
-        _Self = "std::cell::Cell<T>",
+        any(_Self = "core::cell::Cell<T>", _Self = "std::cell::Cell<T>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock`",
     ),
     on(
-        _Self = "std::cell::RefCell<T>",
+        any(_Self = "core::cell::RefCell<T>", _Self = "std::cell::RefCell<T>"),
         note = "if you want to do aliasing and mutation between multiple threads, use `std::sync::RwLock` instead",
     ),
     message = "`{Self}` cannot be shared between threads safely",
diff --git a/library/core/src/ops/index.rs b/library/core/src/ops/index.rs
index 1f1784ec9b255..f4649be54d56f 100644
--- a/library/core/src/ops/index.rs
+++ b/library/core/src/ops/index.rs
@@ -153,7 +153,7 @@ see chapter in The Book <https://doc.rust-lang.org/book/ch08-02-strings.html#ind
 see chapter in The Book <https://doc.rust-lang.org/book/ch08-02-strings.html#indexing-into-strings>"
     ),
     on(
-        _Self = "std::string::String",
+        any(_Self = "alloc::string::String", _Self = "std::string::String"),
         note = "you can use `.chars().nth()` or `.bytes().nth()`
 see chapter in The Book <https://doc.rust-lang.org/book/ch08-02-strings.html#indexing-into-strings>"
     ),
diff --git a/library/core/src/ops/try_trait.rs b/library/core/src/ops/try_trait.rs
index b4f69d0b21309..17625daccbcf9 100644
--- a/library/core/src/ops/try_trait.rs
+++ b/library/core/src/ops/try_trait.rs
@@ -226,8 +226,14 @@ pub trait Try: FromResidual {
     on(
         all(
             from_desugaring = "QuestionMark",
-            _Self = "std::result::Result<T, E>",
-            R = "std::option::Option<std::convert::Infallible>"
+            any(
+                _Self = "core::result::Result<T, E>",
+                _Self = "std::result::Result<T, E>",
+            ),
+            any(
+                R = "core::option::Option<core::convert::Infallible>",
+                R = "std::option::Option<std::convert::Infallible>",
+            )
         ),
         message = "the `?` operator can only be used on `Result`s, not `Option`s, \
             in {ItemContext} that returns `Result`",
@@ -237,7 +243,10 @@ pub trait Try: FromResidual {
     on(
         all(
             from_desugaring = "QuestionMark",
-            _Self = "std::result::Result<T, E>",
+            any(
+                _Self = "core::result::Result<T, E>",
+                _Self = "std::result::Result<T, E>",
+            )
         ),
         // There's a special error message in the trait selection code for
         // `From` in `?`, so this is not shown for result-in-result errors,
@@ -250,8 +259,14 @@ pub trait Try: FromResidual {
     on(
         all(
             from_desugaring = "QuestionMark",
-            _Self = "std::option::Option<T>",
-            R = "std::result::Result<T, E>",
+            any(
+                _Self = "core::option::Option<T>",
+                _Self = "std::option::Option<T>",
+            ),
+            any(
+                R = "core::result::Result<T, E>",
+                R = "std::result::Result<T, E>",
+            )
         ),
         message = "the `?` operator can only be used on `Option`s, not `Result`s, \
             in {ItemContext} that returns `Option`",
@@ -261,7 +276,10 @@ pub trait Try: FromResidual {
     on(
         all(
             from_desugaring = "QuestionMark",
-            _Self = "std::option::Option<T>",
+            any(
+                _Self = "core::option::Option<T>",
+                _Self = "std::option::Option<T>",
+            )
         ),
         // `Option`-in-`Option` always works, as there's only one possible
         // residual, so this can also be phrased strongly.
@@ -273,8 +291,14 @@ pub trait Try: FromResidual {
     on(
         all(
             from_desugaring = "QuestionMark",
-            _Self = "std::ops::ControlFlow<B, C>",
-            R = "std::ops::ControlFlow<B, C>",
+            any(
+                _Self = "core::ops::ControlFlow<B, C>",
+                _Self = "std::ops::ControlFlow<B, C>",
+            ),
+            any(
+                R = "core::ops::ControlFlow<B, C>",
+                R = "std::ops::ControlFlow<B, C>",
+            )
         ),
         message = "the `?` operator in {ItemContext} that returns `ControlFlow<B, _>` \
             can only be used on other `ControlFlow<B, _>`s (with the same Break type)",
@@ -285,7 +309,10 @@ pub trait Try: FromResidual {
     on(
         all(
             from_desugaring = "QuestionMark",
-            _Self = "std::ops::ControlFlow<B, C>",
+            any(
+                _Self = "core::ops::ControlFlow<B, C>",
+                _Self = "std::ops::ControlFlow<B, C>",
+            )
             // `R` is not a `ControlFlow`, as that case was matched previously
         ),
         message = "the `?` operator can only be used on `ControlFlow`s \
diff --git a/library/core/src/slice/index.rs b/library/core/src/slice/index.rs
index 6ef9f9c95e843..e1e3bcc05e74b 100644
--- a/library/core/src/slice/index.rs
+++ b/library/core/src/slice/index.rs
@@ -152,7 +152,10 @@ mod private_slice_index {
 #[rustc_on_unimplemented(
     on(T = "str", label = "string indices are ranges of `usize`",),
     on(
-        all(any(T = "str", T = "&str", T = "std::string::String"), _Self = "{integer}"),
+        all(
+            any(T = "str", T = "&str", T = "alloc::string::String", T = "std::string::String"),
+            _Self = "{integer}"
+        ),
         note = "you can use `.chars().nth()` or `.bytes().nth()`\n\
                 for more information, see chapter 8 in The Book: \
                 <https://doc.rust-lang.org/book/ch08-02-strings.html#indexing-into-strings>"