Files
zooqueenandHanzo Dev ac9676a47a proofs: drive formal/lean library to 0 errors
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]>
2026-06-02 09:31:40 -07:00

88 lines
2.7 KiB
Lean4

/-
Authority Meet-Semilattice
Models authority as a set of capabilities with meet (intersection).
Authority can only NARROW through delegation — never escalate.
Maps to:
- hanzo/iam: RBAC permission sets
- lux/node: validator capability scoping
- zoo/contracts: role-based access control
Properties:
- Meet is commutative, associative, idempotent
- Authority narrows through delegation (monotone)
- Meet is greatest lower bound
-/
import Mathlib.Data.Nat.Defs
import Mathlib.Data.List.Basic
import Mathlib.Tactic
namespace Trust.Authority
/-- A capability: what you're allowed to do -/
inductive Capability where
| shell (user : String)
| exec (command : String)
| build (target : String)
| attest (scope : String)
| sign (keyId : String)
| deploy (env : String)
deriving DecidableEq, Repr
/-- Authority: a set of capabilities (List for simplicity) -/
structure Authority where
capabilities : List Capability
deriving DecidableEq, Repr
/-- No authority -/
def Authority.none : Authority := ⟨[]⟩
/-- Full authority -/
def Authority.all : Authority := ⟨[
.shell "root", .exec "*", .build "*",
.attest "*", .sign "*", .deploy "*"
]⟩
/-- Meet (intersection): only capabilities in BOTH sets -/
def Authority.meet (a b : Authority) : Authority :=
⟨a.capabilities.filter (b.capabilities.contains ·)⟩
/-- Subset ordering -/
def Authority.subset (a b : Authority) : Prop :=
∀ c ∈ a.capabilities, c ∈ b.capabilities
instance : LE Authority where le := Authority.subset
instance : Min Authority where min := Authority.meet
/-- Meet is a lower bound (left): a ⊓ b ≤ a -/
theorem meet_le_left (a b : Authority) : min a b ≤ a := by
intro c hc
simp [Min.min, Authority.meet, List.mem_filter] at hc
exact hc.1
/-- Meet is a lower bound (right): a ⊓ b ≤ b -/
theorem meet_le_right (a b : Authority) : min a b ≤ b := by
intro c hc
simp only [Min.min, Authority.meet, List.mem_filter] at hc
exact List.mem_of_elem_eq_true hc.2
/-- Meet is greatest lower bound -/
theorem meet_glb (a b c : Authority) (hca : c ≤ a) (hcb : c ≤ b) :
c ≤ min a b := by
intro cap hcap
simp only [Min.min, Authority.meet, List.mem_filter]
exact ⟨hca cap hcap, List.elem_eq_true_of_mem (hcb cap hcap)⟩
/-- Authority.none is the bottom element -/
theorem none_is_bottom (a : Authority) : Authority.none ≤ a := by
intro c hc; simp [Authority.none] at hc
/-- DELEGATION NARROWING: delegating authority can only reduce it -/
theorem delegation_narrows (delegator_auth delegated_scope : Authority) :
min delegator_auth delegated_scope ≤ delegator_auth :=
meet_le_left delegator_auth delegated_scope
end Trust.Authority