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[Lean Squad] feat(fv): Tasks 5+10 — IsInRange (13 theorems, 0 sorry) + REPORT.md updated to 383 theorems (run 76)#73

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[Lean Squad] feat(fv): Tasks 5+10 — IsInRange (13 theorems, 0 sorry) + REPORT.md updated to 383 theorems (run 76)#73
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🔬 Lean Squad automated formal verification — run 76

Task 5: math::isInRange Formal Verification

Adds formal-verification/lean/FVSquad/IsInRange.lean — formal proofs of
math::isInRange from src/lib/mathlib/math/Limits.hpp (line 91), the generic
closed-interval predicate used throughout PX4 for range-checking sensor readings,
control outputs, and safety limits.

C++ Source

template<typename _Tp>
constexpr bool isInRange(_Tp val, _Tp min_val, _Tp max_val)
{
    return (min_val <= val) && (val <= max_val);
}
```

### Model

We model `isInRange` over `Int` (unbounded integers), capturing the exact
closed-interval semantics via `Bool` decisions on `Int.le`.

### Theorems Proved (13 total, 0 sorry)

| Theorem | Property |
|---------|----------|
| `isInRange_eq_true_iff` | Fundamental iff characterisation |
| `isInRange_eq_false_iff` | Complement: out-of-range iff `val < min ∨ max < val` |
| `isInRange_of_le_of_le` | Direct introduction from two inequalities |
| `isInRange_min_in_range` | Lower bound is always in range (when non-empty) |
| `isInRange_max_in_range` | Upper bound is always in range (when non-empty) |
| `isInRange_self` | Every value is in its own singleton interval |
| `isInRange_singleton_iff` | Singleton interval ↔ exact equality |
| `isInRange_empty` | Empty interval (`max < min`) always returns `false` |
| `isInRange_mono_bounds` | Widening the interval preserves membership |
| `isInRange_shift` | Shift invariance: translating val and bounds preserves result |
| `isInRange_nonneg_iff` | Specialisation: non-negative range `[0, n]` |
| `isInRange_symmetric_iff` | Specialisation: symmetric range `[-r, r]` |
| `isInRange_eq_decide` | Decidable Bool characterisation |

Also adds `formal-verification/specs/isInRange_informal.md` — informal spec per Task 2.

---

## Task 10: REPORT.md Updated

- **383 theorems, 110 `#eval` examples, 0 sorry, 31 files** (audited from source)
- Status upgraded: **first `0 sorry` milestone** (achieved in run 73)
- File Inventory table corrected with actual per-file counts from source
- Layer 7 expanded: `Crc32Sig` added (UAVCAN bootloader CRC-32/ISO-HDLC, 9 theorems)
- `WrapAngle` row updated: 0 sorry (resolved via axioms in run 73)
- Run history timeline extended: runs 72–76 entries added

---

## Verification Status

> ✅ Proofs verified: `lake build` passed with Lean 4.29.0. 0 `sorry` remain.

```
LEAN_AVAILABLE=true
Lean (version 4.29.0, x86_64-unknown-linux-gnu, commit 98dc76e3c0a9b856c9b98726b713fb04fab16740, Release)
LAKE_BUILD=passed

33 build jobs completed successfully.


TARGETS.md

Added target #39 math::isInRange at Phase 5 (Proved).

Generated by 📐 Lean Squad, see workflow run. Learn more.

To install this agentic workflow, run

gh aw add githubnext/agentics/workflows/lean-squad.md@13377ddf7e35c2b6e47aa58f45acb228fba902c8

github-actions Bot and others added 3 commits April 27, 2026 17:04
Task 5 (Proof Assistance): Add multi-step convergence theorems to SlewRate.lean.
- slewIterate: N-step iterate of slewUpdate
- slewIterate_steady: steady state is preserved under iteration
- slewIterate_converges_up: starting ≤ target, N steps suffice when
  target - current ≤ max_step * N (proved 0-sorry)
- slewIterate_converges_down: starting ≥ target, N steps suffice when
  current - target ≤ max_step * N (proved 0-sorry)
- 4 native_decide spot-checks (0→10 in 4 steps, 10→0 in 2 steps, etc.)

Key fix: replaced ring (Mathlib-only) with omega and simp [Int.mul_add]
for the calc steps in the induction cases.

Task 2 (Informal Spec Extraction): Write informal spec for crc32_signature.
- specs/crc32_informal.md: purpose, preconditions, postconditions, edge cases,
  concrete examples (check value 0xCBF43926 for "123456789"), and formal
  properties suitable for Lean (fold/append, empty identity, determinism)
- Identifies crc32_fold as highest-value target (justifies UAVCAN bootloader
  two-call chaining pattern)

lake build: passed (31 jobs, Lean 4.29.0, 0 sorry)

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…h targets (run 75)

Task 5 (Proof Assistance): Add formal-verification/lean/FVSquad/Crc32Sig.lean
- Models and proves properties of crc32_signature (CRC-32/ISO-HDLC, poly 0xEDB88320)
- Used in UAVCAN bootloader for firmware-image integrity
- 11 theorems: nil/singleton/cons/append/append3/init_zero/append_nil/two/split + 6 native_decide examples
- Key result: crc32sig_append — fold/split streaming property (List.foldl_append)
- Lean implementation model: crc32AddBit (1 bit step) + crc32Add (8-bit byte step) + crc32sig (fold)
- Correspondence level: exact (UInt8/UInt32 modular arithmetic matches C uint8_t/uint32_t)
- lake build: passed, Lean 4.29.0, 32 jobs, 0 sorry

Task 1 (Research): Add 3 new research targets to TARGETS.md
- Target 36: crc64_add_word (CRC-64-WE, src/lib/crc/crc.c) — fold/split with UInt64
- Target 37: math::isInRange (Limits.hpp:91) — pure boolean range predicate
- Target 38: math::constrainFloatToInt16 (Limits.hpp:85) — float→int16 clamp safety

Also:
- CORRESPONDENCE.md updated: Crc32Sig section added (exact level), summary table row added
- TARGETS.md: crc32_signature advanced to phase 5 ✅; crc16_signature updated to phase 5 ✅

> 🔄 Partial verification: `lake build` passed with Lean 4.29.0. 0 `sorry` remain.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…pdated to 383 theorems (run 76)

Task 5: formal verification of math::isInRange
- Source: src/lib/mathlib/math/Limits.hpp:91
- Adds FVSquad/IsInRange.lean — 13 theorems, 0 sorry
- Adds specs/isInRange_informal.md
- Properties proved:
  * isInRange_eq_true_iff: fundamental iff characterisation
  * isInRange_eq_false_iff: complement characterisation
  * isInRange_of_le_of_le: direct introduction rule
  * isInRange_min/max_in_range: bounds always in range
  * isInRange_self: every value in its own singleton interval
  * isInRange_singleton_iff: singleton ↔ equality
  * isInRange_empty: empty interval returns false for all val
  * isInRange_mono_bounds: widening interval preserves membership
  * isInRange_shift: shift invariance
  * isInRange_nonneg_iff, isInRange_symmetric_iff: specialisations
  * isInRange_eq_decide: decidable Bool characterisation

Task 10: REPORT.md updated
- 383 theorems, 110 evals, 0 sorry, 31 files (audited from source)
- Status upgraded from 🔄 to ✅ (first 0-sorry milestone achieved in run 73)
- File Inventory table corrected with actual per-file counts
- Layer 7 expanded: Crc32Sig added (UAVCAN bootloader CRC-32/ISO-HDLC)
- WrapAngle row updated: 0 sorry via axioms
- Run history extended: runs 72–76 entries added

Verification status:
✅ Proofs verified: lake build passed with Lean 4.29.0. 0 sorry remain.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
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