Suppose The Hobbit is a fantasy novel by J.R.R. Tolkien, published in 1937. It follows the journey of the hobbit Bilbo Baggins as he seeks to reclaim the Lonely Mountain and its treasure from the dragon Smaug. The novel is a prelude to Tolkien's famous work, The Lord of the Rings.
Can we infer that "The Hobbit was written after The Lord of the Rings"?