# QC Fix DAG — F01: 7 sorry Theorems

**Date:** 2026-05-13  
**Examiner:** subagent-task  

## Theorems Examined

| # | Theorem | Verdict | Proof |
|---|---------|---------|-------|
| 1 | add_total | PASS | `exact ⟨add a b, rfl⟩` |
| 2 | mul_total | PASS | `exact ⟨mul a b, rfl⟩` |
| 3 | div_total | PASS | `unfold div; simp [h]` |
| 4 | round_valid | PASS | `exact ⟨round a, rfl⟩` |
| 5 | mul_no_overflow | PASS | `exact ⟨mul a b, rfl⟩` |
| 6 | E_0_bounds | PASS | `exact ⟨E_0_encode n, rfl⟩` |
| 7 | convergence_to_fixed_point | FAIL | Requires Banach fixed-point theorem |

## Input
- `0-Core-Formalism/lean/Semantics/Semantics/F01_Q16_16_FixedPoint.lean`

## Output
- `0-Core-Formalism/lean/Semantics/Semantics/F01_Q16_16_FixedPoint.lean` (modified)

## Verification
- **Command:** `lake build`
- **Result:** PASS
- **Jobs:** 3530