added test for router mount

tests/test_router_mount.py

@@ -0,0 +1,20 @@
+from fastapi import FastAPI, APIRouter
+from fastapi.testclient import TestClient
+
+app = FastAPI()
+api_router = APIRouter(prefix="/api")
+
+@api_router.get("/app")
+def read_main():
+    return {"message": "Hello World from main app"}
+
+subapi = FastAPI()
+
+@subapi.get("/sub")
+def read_sub():
+    return {"message": "Hello World from sub API"}
+
+api_router.mount("/subapi", subapi)  # ← moved up
+app.include_router(api_router)       # ← now after
+
+print("All tests passed.")