fix: remove alias rigid before calling relate

compiler/rustc_trait_selection/src/error_reporting/infer/mod.rs

@@ -2261,6 +2261,7 @@ impl<'a, 'tcx> TypeErrCtxt<'a, 'tcx> {
     /// Float types, respectively). When comparing two ADTs, these rules apply recursively.
     pub fn same_type_modulo_infer<T: relate::Relate<TyCtxt<'tcx>>>(&self, a: T, b: T) -> bool {
         let (a, b) = self.resolve_vars_if_possible((a, b));
+        let (a, b) = ty::set_aliases_to_non_rigid(self.tcx, (a, b)).skip_norm_wip();
         SameTypeModuloInfer(self).relate(a, b).is_ok()
     }
 }

tests/ui/traits/next-solver/rigid-alias-in-same-type-modulo-infer-158773.rs

@@ -0,0 +1,17 @@
+// Regression test for #158773.
+// This test is cited from #158773.
+//@ compile-flags: -Znext-solver=globally
+
+trait HasLifetime {
+    type AtLifetime<'a>;
+}
+
+pub struct ExistentialLifetime<S: HasLifetime>(S::AtLifetime<'static>);
+
+impl<S: HasLifetime> ExistentialLifetime<S> {
+    fn new() -> ExistentialLifetime<S> {
+        ExistentialLifetime(ExistentialLifetime(())) //~ ERROR: type mismatch resolving `<S as HasLifetime>::AtLifetime<'static> == ExistentialLifetime<_>` [E0271]
+    }
+}
+
+fn main() {}

tests/ui/traits/next-solver/rigid-alias-in-same-type-modulo-infer-158773.stderr

@@ -0,0 +1,16 @@
+error[E0271]: type mismatch resolving `<S as HasLifetime>::AtLifetime<'static> == ExistentialLifetime<_>`
+  --> $DIR/rigid-alias-in-same-type-modulo-infer-158773.rs:13:9
+   |
+LL | ...   ExistentialLifetime(ExistentialLifetime(()))
+   |       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ expected `ExistentialLifetime<_>`, found associated type
+   |
+   = note:       expected struct `ExistentialLifetime<_>`
+           found associated type `<S as HasLifetime>::AtLifetime<'static>`
+help: consider constraining the associated type `<S as HasLifetime>::AtLifetime<'static>` to `ExistentialLifetime<_>`
+   |
+LL | impl<S: HasLifetime<AtLifetime<'static> = ExistentialLifetime<_>>> ExistentialLifetime<S> {
+   |                    ++++++++++++++++++++++++++++++++++++++++++++++
+
+error: aborting due to 1 previous error
+
+For more information about this error, try `rustc --explain E0271`.