> ## Documentation Index
> Fetch the complete documentation index at: https://cyberpaisa-dof-mesh-40-27.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# CLI: prove & verify-states

> dof prove, dof verify-states, dof verify-hierarchy — Z3 formal verification commands.

## dof prove

Runs all 4 Z3 SMT theorems and reports results.

```bash theme={null}
dof prove
```

```
DOF Formal Verification — Z3 SMT Solver
All verified: True | Total time: 8.6ms

  VERIFIED  GCR_INVARIANT    (3.10ms)
  VERIFIED  SS_FORMULA       (1.80ms)
  VERIFIED  SS_MONOTONICITY  (2.40ms)
  VERIFIED  SS_BOUNDARIES    (1.20ms)
```

**JSON output:**

```bash theme={null}
dof --json prove
```

```json theme={null}
{
  "verified": true,
  "theorems": [
    {"name": "GCR_INVARIANT",   "result": "VERIFIED", "time_ms": 3.10},
    {"name": "SS_FORMULA",      "result": "VERIFIED", "time_ms": 1.80},
    {"name": "SS_MONOTONICITY", "result": "VERIFIED", "time_ms": 2.40},
    {"name": "SS_BOUNDARIES",   "result": "VERIFIED", "time_ms": 1.20}
  ]
}
```

***

## dof verify-states

Verifies 4 state invariants via `TransitionVerifier` across all 9 transition types.

```bash theme={null}
dof verify-states
```

```
DOF State Transition Verification — 4/4 PROVEN

  INV-1: threat_detected → NOT publish_allowed           PROVEN
  INV-2: trust_score < 0.4 → attestation_count == 0     PROVEN
  INV-3: hierarchy_level_next <= hierarchy_level + 1     PROVEN
  INV-4: 0 <= trust_score <= 1                           PROVEN
```

**JSON output:**

```json theme={null}
{
  "proven": true,
  "invariants": [
    {"id": "INV-1", "result": "PROVEN"},
    {"id": "INV-2", "result": "PROVEN"},
    {"id": "INV-3", "result": "PROVEN"},
    {"id": "INV-4", "result": "PROVEN"}
  ],
  "transition_types": 9,
  "time_ms": 110
}
```

***

## dof verify-hierarchy

Verifies the `SYSTEM > USER > ASSISTANT` hierarchy across 42 patterns.

```bash theme={null}
dof verify-hierarchy
```

```
DOF Hierarchy Verification — Z3
  42 patterns PROVEN
  6 override patterns:    all PROVEN
  11 escalation patterns: all PROVEN
  25 hierarchy patterns:  all PROVEN

  verify_hierarchy_inviolable() → PROVEN
  find_weakest_pattern()        → None (all strong)
```

***

## regression-baseline / regression-check

Capture a baseline and check for regressions:

```bash theme={null}
dof regression-baseline
# Baseline captured:
#   Z3 invariants: 4/4 PROVEN
#   Tests:         4,800 passed
#   Timestamp:     2026-04-12T00:00:00Z

dof regression-check
# Comparing vs baseline...
#   Z3 invariants: 4/4 PROVEN ✓
#   Tests:         4,800 passed ✓
#   No regressions detected — exit 0
```

Use in CI:

```bash theme={null}
dof regression-check || exit 1
```

***

## Python API

```python theme={null}
from dof.quick import prove

result = prove()
assert result["verified"] == True
assert all(t["result"] == "VERIFIED" for t in result["theorems"])

for t in result["theorems"]:
    print(f"{t['name']}: {t['result']} ({t['time_ms']}ms)")
```

***

<CardGroup cols={2}>
  <Card title="Formal Verification" icon="function" href="/concepts/formal-verification">
    Theory behind Z3 proofs and invariants
  </Card>

  <Card title="Z3 API Reference" icon="code" href="/reference/z3-api">
    Z3Verifier and TransitionVerifier API
  </Card>
</CardGroup>