∀ (pat : String.Slice) (table : Array ℕ) (guess : ℕ) (hg : guess < table.size) (this : table[guess - 1] < guess),
  InvImage (fun x1 x2 => x1 < x2) (fun x => PSigma.casesOn x fun guess hg => guess) ⟨table[guess - 1], ⋯⟩ ⟨guess, hg⟩