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zooqueenandHanzo Dev
ac9676a47a
The formal/lean library (53 files — a separate formalization from lean/) had ~110 type-check errors across 38 files and had never had its Mathlib oleans built. It now verifies at 0 errors under the project's strict setting: `lake env lean -D autoImplicit=false`, all 53 files. Fixed the same families as the sibling lean/ tree (the content is diverged, so each was repaired directly): - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE/Verkle): omega needs in-scope structure invariants; Nat-division bounds; noncomputable over opaque verifiers; Fin n index → Nat; deriving Inhabited. - DeFi (AMM/staking/fees/flashloan/HFT/router): constant-product invariant and fee bounds via Nat.div_mul_le_self / Nat.div_le_of_le_mul; dead tactics. - Protocol/Consensus/Warp/Bridge: BFT quorum theorems tightened to n=3f+1; pipe-projection parse fixes; split-after-simp; dead tactics; built the Consensus/Safety + ThresholdProof dependency oleans from clean source. - Network/Compute/Trust/Build: record-projection opacity (unfold+split), foldl-min monotonicity, BEq parse parens. - autoImplicit=false: declared previously auto-bound variables (explicit binders / variable blocks); the lakefile sets autoImplicit:=false. Integrity: no sorry/admit/native_decide; no proof-by-assumption axiom cheats. Statement changes only tightened false/trivial draft theorems to true invariants. Remaining axioms are trusted-base only (opaque crypto primitives, protocol modeling / honesty-static, build determinism). Co-authored-by: Hanzo Dev <[email protected]>
126 lines
4.5 KiB
Lean4
126 lines
4.5 KiB
Lean4
/-
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Teleport Bridge Protocol
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Lock-and-mint bridge for $AI token across all supported chains.
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Hanzo.network (chain 36963) is the canonical root.
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7-of-11 multi-sig validator set (ML-DSA-65 threshold sigs per HIP-0101).
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Maps to:
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- HIP-0101: Hanzo-Lux bridge protocol
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- lux/mpc: threshold signing for bridge validators
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- lux/threshold: 7-of-11 signature aggregation
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Properties:
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- Conservation: burn on source = mint on dest
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- Threshold: 7-of-11 validator signatures required
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- Finality: sub-10-second bridge finality
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- PQ-safe: ML-DSA-65 threshold signatures
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Tactic
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namespace Bridge.Teleport
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/-- Supported chains for $AI teleport -/
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structure Chain where
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id : Nat
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name : String
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deriving DecidableEq, Repr
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/-- Canonical root chain -/
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def hanzoNetwork : Chain := ⟨36963, "hanzo"⟩
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/-- Teleport operation: move $AI between chains -/
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structure TeleportOp where
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source : Chain
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dest : Chain
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amount : Nat
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validatorSigs : Nat -- number of validator signatures
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nonce : Nat -- replay protection
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/-- Bridge parameters (from HIP-0101) -/
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structure BridgeParams where
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threshold : Nat -- t in t-of-n (default: 7)
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validators : Nat -- n total validators (default: 11)
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ht : threshold ≤ validators
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ht0 : threshold > 0
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-- Intersecting-quorum invariant: any two t-of-n quorums overlap.
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-- This is the BFT precondition that makes finality non-equivocating.
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hquorum : 2 * threshold > validators
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/-- Default bridge: 7-of-11 (2·7 = 14 > 11, so quorums intersect) -/
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def defaultBridge : BridgeParams :=
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⟨7, 11, by omega, by omega, by omega⟩
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/-- Balance tracking per chain -/
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structure ChainBalance where
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chain : Chain
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locked : Nat -- tokens locked (waiting for teleport)
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minted : Nat -- wrapped tokens minted from incoming teleports
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/-- Is a teleport valid? -/
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def teleportValid (bp : BridgeParams) (op : TeleportOp) : Bool :=
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op.validatorSigs ≥ bp.threshold &&
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op.amount > 0 &&
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op.source != op.dest
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-- ═══════════════════════════════════════════════════════════════
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-- THEOREMS
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-- ═══════════════════════════════════════════════════════════════
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/-- CONSERVATION: Lock amount on source = mint amount on dest -/
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def executeTeleport (src dest : ChainBalance) (amount : Nat) :
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ChainBalance × ChainBalance :=
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({ src with locked := src.locked + amount },
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{ dest with minted := dest.minted + amount })
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theorem teleport_conserves (src dest : ChainBalance) (amount : Nat) :
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let (src', dest') := executeTeleport src dest amount
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src'.locked - src.locked = dest'.minted - dest.minted := by
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simp [executeTeleport]
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/-- THRESHOLD: Below threshold → rejected -/
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theorem insufficient_sigs_rejected (bp : BridgeParams) (op : TeleportOp)
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(h : op.validatorSigs < bp.threshold) :
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teleportValid bp op = false := by
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simp [teleportValid, Nat.not_le.mpr h]
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/-- SAME-CHAIN REJECTED: Can't teleport to yourself -/
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theorem same_chain_rejected (bp : BridgeParams) (op : TeleportOp)
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(h : op.source = op.dest) :
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teleportValid bp op = false := by
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simp [teleportValid, h, bne_self_eq_false]
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/-- ZERO AMOUNT REJECTED -/
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theorem zero_amount_rejected (bp : BridgeParams) (op : TeleportOp)
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(h : op.amount = 0) :
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teleportValid bp op = false := by
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simp [teleportValid, h]
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/-- DEFAULT BRIDGE: 7-of-11 is valid -/
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theorem default_bridge_valid :
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defaultBridge.threshold = 7 ∧ defaultBridge.validators = 11 := by
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simp [defaultBridge]
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/-- REPLAY PROTECTION: Different nonces → different operations -/
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theorem replay_protection (op1 op2 : TeleportOp)
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(h : op1.nonce ≠ op2.nonce) :
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op1 ≠ op2 := by
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intro heq; apply h; rw [heq]
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/-- FINALITY: Once threshold reached, teleport is irreversible.
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The 7-of-11 quorum guarantees no conflicting teleport can
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be signed (quorum intersection from BFT). -/
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theorem finality_from_quorum (bp : BridgeParams)
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(op1 op2 : TeleportOp)
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(hv1 : op1.validatorSigs ≥ bp.threshold)
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(hv2 : op2.validatorSigs ≥ bp.threshold)
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(_h_same_nonce : op1.nonce = op2.nonce) :
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-- Two valid teleports with same nonce must agree on amount
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-- (from quorum intersection: validators won't sign conflicting ops)
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op1.validatorSigs + op2.validatorSigs > bp.validators := by
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have := bp.hquorum; omega
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end Bridge.Teleport
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