proven-bounds

To convert runtime bounds checks to proven bounds in Lean 4, you transform unsafe access patterns like `xs[i]!` into static bounds like `xs[i]` using guard capture, loop bound capture, and caller propagation techniques.

Guard capture in Lean 4 is a technique that implements conditional bounds checks using `if h :` syntax, capturing the proof context needed to safely replace runtime checks with static, proven bounds.

You capture loop index bounds in Lean 4 using the `for h : i in` syntax, which allows the loop structure to retain the index bounds proof needed for safe array access without runtime checks.

Yes, converting runtime bounds checks to proven bounds in Lean 4 requires existing knowledge of Lean 4 and its proof techniques, specifically for writing termination proofs and bounds justifications.

Using proven bounds instead of runtime bounds checks in Lean 4 eliminates runtime overhead and ensures code safety and reliability by statically guaranteeing that array accesses are always within valid limits.