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zooqueenandHanzo Dev
d3bff5e2dc
The lean/ proof library (88 files) had ~180 type-check errors across ~45 files plus 31 proof-by-assumption axiom cheats. It now type-checks cleanly under Lean 4.14.0 + Mathlib, with every theorem genuinely proven from definitions. Errors fixed: - Stale Mathlib imports: Data.Nat.Basic / Data.Int.Basic were removed this rev -> Data.Nat.Defs / Data.Int.Defs (57 files). - Shared AI/Agent/Governance/Contract/DeFi/Ecology draft files: same proof-rot as the zoo-labs sibling library (now reconciled): omega missing in-scope bounds, dead tactics after simp, simp over-reduction, doc-comment placement, reserved-word binders, deriving Repr on Finset-bearing structs, noncomputable defs over opaque primitives. - Consensus/Liveness: collapsed a 74-error cascade (undefined shared state model inlined from Safety.lean; the |>. pipe-projection vs comparison parse trap on 14 lines rewritten to explicit dot projection). - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE), Consensus, Protocol, Warp, Trust, GPU, Compute, Network, DeFi: brought structure invariants into scope for omega, Nat-division bounds via Nat.div_le_of_le_mul / Nat.div_mul_le_self, noncomputable over opaque crypto ops, deriving Inhabited for index access. Integrity: - Removed all 31 `theorem X := X_ax` cheats (axiom asserting the identical statement) and proved each from definitions; removed the UNSOUND content_addressed axiom (hash-injectivity over a struct with free fields). - Quorum-intersection theorems (BFT/Quasar/Flare/Warp/BLS/GPU/Bridge): the draft hypothesis 3f<n is insufficient (n unbounded above makes them false); tightened to the optimal-resilience invariant n=3f+1 / 2t>n. Statement intent preserved. - Net axiom change: -35 / +1 (the one addition, honesty_static, is a fixed-validator-set modeling assumption matching sibling files). - Remaining axioms are trusted-base only: opaque crypto primitives (groups, pairings, hardness, hashes, FHE encrypt/decrypt, BLS soundness, forward secrecy, Fisher-Yates uniformity) and protocol modeling assumptions. No sorry/admit/native_decide. Verified all theorems trace to [propext, Classical.choice, Quot.sound] plus those primitives. Co-authored-by: Hanzo Dev <[email protected]>
93 lines
2.8 KiB
Lean4
93 lines
2.8 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Authority Meet-Semilattice
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Models authority as a set of capabilities with meet (intersection).
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Authority can only NARROW through delegation — never escalate.
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Maps to:
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- hanzo/iam: RBAC permission sets
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- lux/node: validator capability scoping
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- zoo/contracts: role-based access control
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Properties:
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- Meet is commutative, associative, idempotent
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- Authority narrows through delegation (monotone)
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- Meet is greatest lower bound
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Tactic
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namespace Trust.Authority
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/-- A capability: what you're allowed to do -/
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inductive Capability where
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| shell (user : String)
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| exec (command : String)
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| build (target : String)
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| attest (scope : String)
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| sign (keyId : String)
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| deploy (env : String)
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deriving DecidableEq, Repr
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/-- Authority: a set of capabilities (List for simplicity) -/
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structure Authority where
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capabilities : List Capability
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deriving DecidableEq, Repr
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/-- No authority -/
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def Authority.none : Authority := ⟨[]⟩
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/-- Full authority -/
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def Authority.all : Authority := ⟨[
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.shell "root", .exec "*", .build "*",
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.attest "*", .sign "*", .deploy "*"
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]⟩
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/-- Meet (intersection): only capabilities in BOTH sets -/
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def Authority.meet (a b : Authority) : Authority :=
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⟨a.capabilities.filter (b.capabilities.contains ·)⟩
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/-- Subset ordering -/
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def Authority.subset (a b : Authority) : Prop :=
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∀ c ∈ a.capabilities, c ∈ b.capabilities
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instance : LE Authority where le := Authority.subset
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instance : Min Authority where min := Authority.meet
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/-- Meet is a lower bound (left): a ⊓ b ≤ a -/
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theorem meet_le_left (a b : Authority) : min a b ≤ a := by
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intro c hc
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simp [Min.min, Authority.meet, List.mem_filter] at hc
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exact hc.1
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/-- Meet is a lower bound (right): a ⊓ b ≤ b -/
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theorem meet_le_right (a b : Authority) : min a b ≤ b := by
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intro c hc
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simp only [Min.min, Authority.meet, List.mem_filter, List.contains_eq_any_beq,
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List.any_eq_true, beq_iff_eq] at hc
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obtain ⟨_, x, hxb, hcx⟩ := hc
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rw [hcx]; exact hxb
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/-- Meet is greatest lower bound -/
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theorem meet_glb (a b c : Authority) (hca : c ≤ a) (hcb : c ≤ b) :
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c ≤ min a b := by
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intro cap hcap
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simp only [Min.min, Authority.meet, List.mem_filter, List.contains_eq_any_beq,
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List.any_eq_true, beq_iff_eq]
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exact ⟨hca cap hcap, cap, hcb cap hcap, rfl⟩
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/-- Authority.none is the bottom element -/
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theorem none_is_bottom (a : Authority) : Authority.none ≤ a := by
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intro c hc; simp [Authority.none] at hc
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/-- DELEGATION NARROWING: delegating authority can only reduce it -/
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theorem delegation_narrows (delegator_auth delegated_scope : Authority) :
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min delegator_auth delegated_scope ≤ delegator_auth :=
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meet_le_left delegator_auth delegated_scope
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end Trust.Authority
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