diff --git a/src/analyze/annot_fn.rs b/src/analyze/annot_fn.rs
index aa733308..b6abfb43 100644
--- a/src/analyze/annot_fn.rs
+++ b/src/analyze/annot_fn.rs
@@ -213,8 +213,11 @@ impl<'a, 'tcx> AnnotFnTranslator<'a, 'tcx> {
         for (idx, param) in self.body.params.iter().enumerate() {
             let param_idx = rty::FunctionParamIdx::from(idx);
             let mir_ty = self.pat_ty(param.pat);
-            let ty = self.type_builder.build(mir_ty);
-            let term = if !self.is_fn_param_wrapper_ty(mir_ty) && ty.to_sort().is_singleton() {
+            // `at_entry()` yields the `Inner` of a `FnParam<Inner>`; classify by it so
+            // a singleton wrapped argument collapses like any other singleton below.
+            let repr_ty = self.fn_param_wrapper_inner_ty(mir_ty).unwrap_or(mir_ty);
+            let ty = self.type_builder.build(repr_ty);
+            let term = if ty.to_sort().is_singleton() {
                 // the analyzer don't expect params with singleton sorts to be used in formula...
                 // FIXME: fix the analyzer side to uniformly accept all params
                 Self::singleton_term_for_ty(&ty).unwrap()
@@ -259,9 +262,16 @@ impl<'a, 'tcx> AnnotFnTranslator<'a, 'tcx> {
         }
     }
 
-    fn is_fn_param_wrapper_ty(&self, ty: mir_ty::Ty<'tcx>) -> bool {
-        ty.ty_adt_def()
-            .is_some_and(|def| Some(def.did()) == self.def_ids.fn_param_wrapper())
+    /// The `Inner` of a `thrust_models::FnParam<Inner>` wrapper type, if `ty` is one.
+    fn fn_param_wrapper_inner_ty(&self, ty: mir_ty::Ty<'tcx>) -> Option<mir_ty::Ty<'tcx>> {
+        match ty.kind() {
+            mir_ty::TyKind::Adt(def, args)
+                if Some(def.did()) == self.def_ids.fn_param_wrapper() =>
+            {
+                Some(args.type_at(0))
+            }
+            _ => None,
+        }
     }
 
     fn build_env_from_pat(
diff --git a/tests/ui/fail/loop_invariant_fn_param_closure.rs b/tests/ui/fail/loop_invariant_fn_param_closure.rs
new file mode 100644
index 00000000..c808b111
--- /dev/null
+++ b/tests/ui/fail/loop_invariant_fn_param_closure.rs
@@ -0,0 +1,50 @@
+//@error-in-other-file: Unsat
+//@compile-flags: -C debug-assertions=off
+
+// A loop invariant refers to a closure parameter via `FnParam<F>`, whose
+// `f.at_entry()` yields `Closure<F>`. Here the invariant relates `acc` to the
+// entry closure's postcondition, from which the postcondition below is proven.
+#[thrust_macros::ensures((n > 0) ==> thrust_macros::post!(f(n - 1), result))]
+#[thrust_macros::invariant_context]
+fn last_apply<F>(f: F, n: i64) -> i64
+where
+    F: Fn(i64) -> i64,
+{
+    let mut acc = 0_i64;
+    let mut i = 0_i64;
+    while i < n {
+        thrust_macros::invariant!(
+            |i: i64, acc: i64, f: thrust_models::FnParam<F>|
+            (i > 0) ==> thrust_macros::post!(f.at_entry()(i - 1), acc)
+        );
+        acc = f(i);
+        i += 1;
+    }
+    acc
+}
+
+// A capture-free closure is null (singleton) sorted; comparing its identity
+// must collapse to a canonical value rather than ICE during clause building.
+#[thrust_macros::invariant_context]
+fn unchanged<F>(mut f: F)
+where
+    F: FnMut(i64) -> i64,
+{
+    let _ = &mut f;
+    let mut i = 0_i64;
+    while i < 10 {
+        thrust_macros::invariant!(
+            |i: i64, f: thrust_models::FnParam<F>|
+            f.at_entry() == f.at_entry() && i <= 10
+        );
+        i += 1;
+    }
+    assert!(i == 11); // Unsat: the loop exits with i == 10
+}
+
+fn main() {
+    let c = 7_i64;
+    let _ = last_apply(|x| x + c, 10);
+
+    unchanged(|x| x + 1);
+}
diff --git a/tests/ui/pass/loop_invariant_fn_param_closure.rs b/tests/ui/pass/loop_invariant_fn_param_closure.rs
new file mode 100644
index 00000000..79d3928f
--- /dev/null
+++ b/tests/ui/pass/loop_invariant_fn_param_closure.rs
@@ -0,0 +1,50 @@
+//@check-pass
+//@compile-flags: -C debug-assertions=off
+
+// A loop invariant refers to a closure parameter via `FnParam<F>`, whose
+// `f.at_entry()` yields `Closure<F>`. Here the invariant relates `acc` to the
+// entry closure's postcondition, from which the postcondition below is proven.
+#[thrust_macros::ensures((n > 0) ==> thrust_macros::post!(f(n - 1), result))]
+#[thrust_macros::invariant_context]
+fn last_apply<F>(f: F, n: i64) -> i64
+where
+    F: Fn(i64) -> i64,
+{
+    let mut acc = 0_i64;
+    let mut i = 0_i64;
+    while i < n {
+        thrust_macros::invariant!(
+            |i: i64, acc: i64, f: thrust_models::FnParam<F>|
+            (i > 0) ==> thrust_macros::post!(f.at_entry()(i - 1), acc)
+        );
+        acc = f(i);
+        i += 1;
+    }
+    acc
+}
+
+// A capture-free closure is null (singleton) sorted; comparing its identity
+// must collapse to a canonical value rather than ICE during clause building.
+#[thrust_macros::invariant_context]
+fn unchanged<F>(mut f: F)
+where
+    F: FnMut(i64) -> i64,
+{
+    let _ = &mut f;
+    let mut i = 0_i64;
+    while i < 10 {
+        thrust_macros::invariant!(
+            |i: i64, f: thrust_models::FnParam<F>|
+            f.at_entry() == f.at_entry() && i <= 10
+        );
+        i += 1;
+    }
+    assert!(i == 10);
+}
+
+fn main() {
+    let c = 7_i64;
+    let _ = last_apply(|x| x + c, 10);
+
+    unchanged(|x| x + 1);
+}
diff --git a/thrust-macros/src/formula_fn_type_lowering.rs b/thrust-macros/src/formula_fn_type_lowering.rs
index 1111ba7e..faac646b 100644
--- a/thrust-macros/src/formula_fn_type_lowering.rs
+++ b/thrust-macros/src/formula_fn_type_lowering.rs
@@ -192,6 +192,19 @@ impl<'a> FormulaFnTypeLowering<'a> {
                     .collect();
                 syn::Type::Tuple(tt)
             }
+            syn::Type::Path(tp) => {
+                let mut tp = tp.clone();
+                for segment in &mut tp.path.segments {
+                    if let syn::PathArguments::AngleBracketed(args) = &mut segment.arguments {
+                        for arg in &mut args.args {
+                            if let syn::GenericArgument::Type(elem) = arg {
+                                *elem = self.lower_closure_type_params_in_ty(elem);
+                            }
+                        }
+                    }
+                }
+                syn::Type::Path(tp)
+            }
             // TODO: support more types including ADT
             _ => ty.clone(),
         }