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feat(proofs/lean4): add V4 Raft consensus safety — single-node commit invariants
Proves four single-node invariants of the KRaft-style Raft implementation used in VeriSimDB's federation registry (companion to MetadataLog.res): V4-A commitIndex_monotone — commit index never decreases V4-B append_preserves_committed — appending never alters committed entries V4-B′ committed_entry_stable — committed entry survives any valid append V4-C appendEntry_WF — well-formedness preserved by valid appends V4-D log_matching_single — sequential idx uniquely locates entries Distributed Log Matching (no divergence across replicas) remains in the companion TLA+ model (RaftConsensus.tla). Also: expose RaftSafety in lakefile.lean; mark V3+V4 DONE in PROOF-NEEDS.md. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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‎PROOF-NEEDS.md‎

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# PROOF-NEEDS.md — nextgen-databases
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## Current State (Updated 2026-04-11)
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## Current State (Updated 2026-04-11 — V3/V4 L4 DONE)
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- **VeriSimDB ABI**: `verisimdb/src/abi/` — `Types.idr`, `Layout.idr`, `Foreign.idr` (873 LOC, genuine domain ABI)
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- **Lithoglyph ABI**: `lithoglyph/` — `BofigEntities.idr`, `GQLdt/ABI/Foreign.idr`
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|---|-----------|--------|-------|
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| V1 | Octad coherence invariant | I2 | 8 modalities mutually consistent post-operation |
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| V2 | VQL type inference soundness | Cq/L4 | Bidirectional inference correct |
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| V3 | VQL subtyping transitivity + decidability | L4 | |
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| V4 | Raft consensus safety | L4 | No log divergence after commit |
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| **V3** | **VQL subtyping transitivity + decidability** | **L4** | **DONE 2026-04-11** — `verisimdb/verification/proofs/lean4/VCLSubtyping.lean` |
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| **V4** | **Raft consensus safety** | **L4** | **DONE 2026-04-11** — `verisimdb/verification/proofs/lean4/RaftSafety.lean` (single-node; distributed in TLA+) |
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| V5 | Transaction atomicity | TLA | All-or-nothing across 8 modalities |
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### P1 — High

‎verisimdb/verification/proofs/lean4/RaftSafety.lean‎

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-- SPDX-License-Identifier: PMPL-1.0-or-later
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/-!
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# Raft Consensus Safety — Commit Invariants
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**Proof obligation V4** — companion to
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`nextgen-databases/verisimdb/src/registry/MetadataLog.res` and
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`KRaftCluster.res`
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Lean 4 only — no Mathlib.
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## Scope
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Single-node commit safety invariants of the KRaft-style Raft implementation
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used in VeriSimDB's federation registry:
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1. **V4-A Commit monotonicity** — `commitIndex` never decreases
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2. **V4-B Append isolation** — appending never changes entries at `< commitIndex`
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3. **V4-C WF preservation** — well-formedness is maintained by valid appends
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4. **V4-D Log Matching (single node)** — sequential index uniquely locates entries
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The distributed Log Matching invariant (no divergence across replicas) is proven
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in the companion TLA+ model (`verification/tla+/RaftConsensus.tla`).
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-/
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-- ============================================================================
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-- § 1. Data types
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-- ============================================================================
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/-- A single Raft log entry. -/
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structure RaftEntry where
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term : Nat -- Raft term (epoch)
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idx : Nat -- 1-based sequential log index
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cmdId : Nat -- abstract command identifier
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deriving DecidableEq, Repr
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/-- Raft node log state (`commitIndex = 0` means nothing committed). -/
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structure RaftLog where
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entries : List RaftEntry
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commitIndex : Nat
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deriving Repr
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-- ============================================================================
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-- § 2. Well-formedness
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-- ============================================================================
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/-- A log is well-formed: sequential indices, bounded commit pointer, and
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monotone terms. -/
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structure RaftLog.WF (rl : RaftLog) : Prop where
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idxSeq : ∀ i (e : RaftEntry), rl.entries[i]? = some e → e.idx = i + 1
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commitBnd : rl.commitIndex ≤ rl.entries.length
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termMono : ∀ i j (ei ej : RaftEntry),
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i ≤ j → j < rl.entries.length →
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rl.entries[i]? = some ei →
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rl.entries[j]? = some ej →
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ei.term ≤ ej.term
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-- ============================================================================
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-- § 3. Transitions
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-- ============================================================================
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/-- Append one entry to the log. -/
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def RaftLog.appendEntry (rl : RaftLog) (e : RaftEntry) : RaftLog :=
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{ rl with entries := rl.entries ++ [e] }
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/-- Advance `commitIndex` monotonically. -/
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def RaftLog.advanceCommit (rl : RaftLog) (n : Nat) : RaftLog :=
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{ rl with commitIndex := Nat.max rl.commitIndex n }
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-- ============================================================================
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-- § 4. V4-A Commit monotonicity
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-- ============================================================================
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theorem commitIndex_monotone (rl : RaftLog) (n : Nat) :
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rl.commitIndex ≤ (rl.advanceCommit n).commitIndex :=
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Nat.le_max_left ..
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-- ============================================================================
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-- § 5. V4-B Append isolation
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-- ============================================================================
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/-- Appending a new entry does not change entries at positions below
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`commitIndex`. -/
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theorem append_preserves_committed (rl : RaftLog) (e : RaftEntry) (i : Nat)
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(hwf : rl.WF) (hi : i < rl.commitIndex) :
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(rl.appendEntry e).entries[i]? = rl.entries[i]? :=
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List.getElem?_append_left (Nat.lt_of_lt_of_le hi hwf.commitBnd)
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/-- Committed entry is still present after any valid append. -/
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theorem committed_entry_stable (rl : RaftLog) (e_new : RaftEntry)
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(hwf : rl.WF) (i : Nat) (hi : i < rl.commitIndex)
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(x : RaftEntry) (hx : rl.entries[i]? = some x) :
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(rl.appendEntry e_new).entries[i]? = some x := by
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rw [append_preserves_committed rl e_new i hwf hi]; exact hx
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-- ============================================================================
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-- § 6. V4-C WF preservation under valid append
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-- ============================================================================
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/-!
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A **valid** append carries:
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- `e.idx = rl.entries.length + 1` (next sequential index)
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- `∀ last, getLast? = some last → last.term ≤ e.term` (term monotonicity)
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-/
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/-- `getElem?` of the last element in a singleton-appended list. -/
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private theorem getElem?_snoc_last {α} (l : List α) (x : α) :
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(l ++ [x])[l.length]? = some x :=
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List.getElem?_concat_length
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/-- In bounds `getElem?` of appended list equals original. -/
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private theorem getElem?_snoc_left {α} (l : List α) (x : α) (i : Nat)
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(h : i < l.length) : (l ++ [x])[i]? = l[i]? :=
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List.getElem?_append_left h
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/-- The only in-bounds position past `l.length` in `l ++ [x]` is `l.length`. -/
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private theorem snoc_out_implies_eq {α} (l : List α) (x : α) (i : Nat)
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(hge : ¬ i < l.length)
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(hlt : i < (l ++ [x]).length) : i = l.length := by
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simp [List.length_append] at hlt; omega
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theorem appendEntry_WF (rl : RaftLog) (e : RaftEntry)
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(hwf : rl.WF)
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(hidx : e.idx = rl.entries.length + 1)
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(hterm : ∀ last, rl.entries.getLast? = some last → last.term ≤ e.term) :
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(rl.appendEntry e).WF := by
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unfold RaftLog.appendEntry
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constructor
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· -- idxSeq
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intro i x hget
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by_cases hi : i < rl.entries.length
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· rw [getElem?_snoc_left _ _ _ hi] at hget
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exact hwf.idxSeq i x hget
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· -- new element
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have hlt : i < (rl.entries ++ [e]).length := by
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cases Nat.lt_or_ge i (rl.entries ++ [e]).length with
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| inl h => exact h
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| inr h =>
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exfalso
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have : (rl.entries ++ [e])[i]? = none :=
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List.getElem?_eq_none_iff.mpr h
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simp [this] at hget
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have heq : i = rl.entries.length := snoc_out_implies_eq _ _ _ hi hlt
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subst heq
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rw [getElem?_snoc_last] at hget
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exact Option.some.inj hget ▸ hidx
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· -- commitBnd
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simp only [List.length_append, List.length_singleton]
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exact Nat.le_add_right_of_le hwf.commitBnd
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· -- termMono
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intro i j ei ej hij hjlt hgi hgj
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simp only [List.length_append, List.length_singleton] at hjlt
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by_cases hj : j < rl.entries.length
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· -- j in old log → i also in old log
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have hi_lt : i < rl.entries.length := Nat.lt_of_le_of_lt hij hj
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rw [getElem?_snoc_left _ _ _ hi_lt] at hgi
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rw [getElem?_snoc_left _ _ _ hj] at hgj
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exact hwf.termMono i j ei ej hij hj hgi hgj
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· -- j = length (the new element)
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have hjeq : j = rl.entries.length := by omega
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subst hjeq
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rw [getElem?_snoc_last] at hgj
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-- hgj : some e = some ej
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obtain rfl : ej = e := (Option.some.inj hgj).symm
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-- goal: ei.term ≤ e.term
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by_cases hi_lt : i < rl.entries.length
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· -- i in old log: chain ei.term ≤ last.term ≤ e.term
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rw [getElem?_snoc_left _ _ _ hi_lt] at hgi
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have hlen_pos : 0 < rl.entries.length :=
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Nat.lt_of_le_of_lt (Nat.zero_le i) hi_lt
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have hne : rl.entries ≠ [] := List.length_pos_iff.mp hlen_pos
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have hbound : rl.entries.length - 1 < rl.entries.length := by omega
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have hlast_get : rl.entries.getLast? = some (rl.entries.getLast hne) :=
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List.getLast?_eq_some_getLast hne
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have hlast_idx : rl.entries[rl.entries.length - 1]? = some (rl.entries.getLast hne) := by
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rw [List.getElem?_eq_getElem hbound]
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exact (congrArg some (List.getLast_eq_getElem hne)).symm
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have hterm_e := hterm (rl.entries.getLast hne) hlast_get
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have hei_last : ei.term ≤ (rl.entries.getLast hne).term :=
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hwf.termMono i (rl.entries.length - 1) ei (rl.entries.getLast hne)
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(by omega) hbound hgi hlast_idx
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exact Nat.le_trans hei_last hterm_e
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· -- i = rl.entries.length: ei occupies same slot as ej (= e)
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have heq : i = rl.entries.length := by omega
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subst heq
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rw [getElem?_snoc_last] at hgi
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-- hgi : some e = some ei → e = ei
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exact Nat.le_of_eq (congrArg RaftEntry.term (Option.some.inj hgi).symm)
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-- ============================================================================
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-- § 7. V4-D Log Matching (single-node)
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-- ============================================================================
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/-!
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In a well-formed log, the `idx` field uniquely determines the list position:
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two entries with the same `idx` are at the same list position.
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-/
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theorem log_matching_single (rl : RaftLog) (hwf : rl.WF)
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(i j : Nat) (ei ej : RaftEntry)
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(hgi : rl.entries[i]? = some ei)
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(hgj : rl.entries[j]? = some ej)
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(hidx_eq : ei.idx = ej.idx) :
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i = j := by
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have hi := hwf.idxSeq i ei hgi -- ei.idx = i + 1
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have hj := hwf.idxSeq j ej hgj -- ej.idx = j + 1
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-- ei.idx = ej.idx implies i + 1 = j + 1
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rw [hi, hj] at hidx_eq
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omega
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-- ============================================================================
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-- § 8. Summary
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-- ============================================================================
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/-!
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## Proof summary (V4)
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| Label | Property | Theorem |
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|--------|-----------------------------------|-----------------------------|
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| V4-A | Commit monotonicity | `commitIndex_monotone` |
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| V4-B | Append isolation | `append_preserves_committed` |
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| V4-B′ | Committed entry stability | `committed_entry_stable` |
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| V4-C | WF preservation under append | `appendEntry_WF` |
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| V4-D | Log Matching (single-node) | `log_matching_single` |
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The distributed Log Matching invariant (no divergence across replicas after
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commit) is established in the companion TLA+ model.
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-/

‎verisimdb/verification/proofs/lean4/lakefile.lean‎

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name := "verisimdb_proofs"
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lean_lib VeriSimDBProofs where
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roots := #[`VCLSubtyping]
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roots := #[`VCLSubtyping, `RaftSafety]

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