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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]>
88 lines
2.7 KiB
Lean4
88 lines
2.7 KiB
Lean4
/-
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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] at hc
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exact List.mem_of_elem_eq_true hc.2
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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]
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exact ⟨hca cap hcap, List.elem_eq_true_of_mem (hcb cap hcap)⟩
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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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