Ledger.Conway.Conformance.Certs

{-# OPTIONS --safe #-}

open import Ledger.Prelude
open import Ledger.Conway.Specification.Gov.Base
import Ledger.Conway.Specification.Certs

module Ledger.Conway.Conformance.Certs
  (gs : _) (open GovStructure gs)
  where


open import Ledger.Conway.Specification.Gov.Actions gs
private module Certs = Ledger.Conway.Specification.Certs gs
open Certs public
  hiding (DState; GState; CertState; HasCast-DState; HasCast-GState; HasCast-CertState;
          _⊢_⇀⦇_,DELEG⦈_; _⊢_⇀⦇_,GOVCERT⦈_;
          _⊢_⇀⦇_,CERT⦈_; _⊢_⇀⦇_,PRE-CERT⦈_; _⊢_⇀⦇_,POST-CERT⦈_; _⊢_⇀⦇_,CERTS⦈_; ⟦_,_,_⟧ᵈ)
open RewardAddress

record DState : Type where
  constructor ⟦_,_,_,_⟧ᵈ
  field
    voteDelegs   : VoteDelegs
    stakeDelegs  : Credential ⇀ KeyHash
    rewards      : Rewards
    deposits     : Deposits

record GState : Type where
  constructor ⟦_,_,_⟧ᵛ
  field
    dreps      : Credential ⇀ Epoch
    ccHotKeys  : Credential ⇀ Maybe Credential
    deposits   : Deposits

record CertState : Type where
  constructor ⟦_,_,_⟧ᶜˢ
  field
    dState : DState
    pState : PState
    gState : GState

instance
  unquoteDecl HasCast-DState HasCast-GState HasCast-CertState = derive-HasCast
    (   (quote DState , HasCast-DState)
    ∷   (quote GState , HasCast-GState)
    ∷ [ (quote CertState , HasCast-CertState) ])

certDeposit : DCert → PParams → Deposits
certDeposit (delegate c _ _ v) _   = ❴ CredentialDeposit c , v ❵
certDeposit (regdrep c v _)    _   = ❴ DRepDeposit c , v ❵
certDeposit (reg c v)          pp  = ❴ CredentialDeposit c , pp .PParams.keyDeposit ❵
certDeposit _                  _   = ∅
-- handled in the Utxo module:
-- certDeposit (regpool kh _)     pp  = ❴ PoolDeposit kh , pp .poolDeposit ❵

certRefund : DCert → ℙ DepositPurpose
certRefund (dereg c _)      = ❴ CredentialDeposit c ❵
certRefund (deregdrep c _)  = ❴ DRepDeposit c ❵
certRefund _                = ∅

updateCertDeposit  : PParams → DCert → Deposits → Deposits
updateCertDeposit pp (delegate c _ _ v) deposits = deposits ∪⁺ ❴ CredentialDeposit c , v ❵
updateCertDeposit pp (reg c _)          deposits = deposits ∪⁺ ❴ CredentialDeposit c , pp .PParams.keyDeposit ❵
updateCertDeposit pp (regdrep c v _)    deposits = deposits ∪⁺ ❴ DRepDeposit c , v ❵
updateCertDeposit pp (dereg c _)        deposits = deposits ∣ ❴ CredentialDeposit c ❵ ᶜ
updateCertDeposit pp (deregdrep c _)    deposits = deposits ∣ ❴ DRepDeposit c ❵ ᶜ
updateCertDeposit pp (regpool kh _)     deposits = deposits ∪⁺ ❴ PoolDeposit kh , pp .PParams.poolDeposit ❵
updateCertDeposit _ (retirepool _ _)    deposits = deposits
updateCertDeposit _ (ccreghot _ _)      deposits = deposits
-- updateCertDeposit pp cert deposits
--   = (deposits ∪⁺ certDeposit cert pp) ∣ certRefund cert ᶜ

private variable
  rwds rewards           : Rewards
  dReps                  : Credential ⇀ Epoch
  sDelegs stakeDelegs    : Credential ⇀ KeyHash
  ccKeys ccHotKeys       : Credential ⇀ Maybe Credential
  vDelegs voteDelegs     : VoteDelegs
  pools fPools           : Pools
  retiring               : KeyHash ⇀ Epoch
  wdrls                  : Withdrawals

  an             : Anchor
  Γ              : CertEnv
  d              : Coin
  md             : Maybe Coin
  c              : Credential
  mc             : Maybe Credential
  delegatees cc  : ℙ Credential
  dCert          : DCert
  dep ddep gdep  : Deposits
  e              : Epoch
  vs             : List GovVote
  kh             : KeyHash
  mkh            : Maybe KeyHash
  poolParams     : StakePoolParams
  pp             : PParams
  mv             : Maybe VDeleg

  stᵈ stᵈ' : DState
  stᵍ stᵍ' : GState
  stᵖ stᵖ' : PState

open GovVote

data _⊢_⇀⦇_,DELEG⦈_ : DelegEnv → DState → DCert → DState → Type

data _⊢_⇀⦇_,DELEG⦈_ where
  DELEG-delegate : let open PParams pp in
    ∙ (c ∉ dom rwds → d ≡ keyDeposit)
    ∙ (c ∈ dom rwds → d ≡ 0)
    ∙ mv ∈ mapˢ (just ∘ vDelegCredential) delegatees ∪
        fromList
          ( nothing
          ∷ just vDelegAbstain
          ∷ just vDelegNoConfidence
          ∷ []
          )
    ∙ mkh ∈ mapˢ just (dom pools) ∪ ❴ nothing ❵
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{4097}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{4102}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3246}{\htmlId{4110}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2919}{\htmlId{4133}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2814}{\htmlId{4143}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2733}{\htmlId{4153}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{4160}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
      ⇀⦇ delegate c mv mkh d ,DELEG⦈
      $\begin{pmatrix} \,\href{Axiom.Set.Map.html#9262}{\htmlId{4211}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4224}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3510}{\htmlId{4226}{\htmlClass{Generalizable}{\text{mv}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2919}{\htmlId{4229}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#9262}{\htmlId{4239}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4252}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3415}{\htmlId{4254}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2814}{\htmlId{4258}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2733}{\htmlId{4268}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{4273}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4276}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4278}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{4282}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4284}{\htmlClass{Field Operator}{\text{❵}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1869}{\htmlId{4294}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{4312}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{4315}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2137}{\htmlId{4316}{\htmlClass{InductiveConstructor}{\text{delegate}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4325}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3510}{\htmlId{4327}{\htmlClass{Generalizable}{\text{mv}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3415}{\htmlId{4330}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3126}{\htmlId{4334}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{4335}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{4337}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  DELEG-dereg :
    ∙ (c , 0) ∈ rwds
    ∙ (CredentialDeposit c , d) ∈ dep
    ∙ md ≡ nothing ⊎ md ≡ just d
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{4499}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{4504}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3246}{\htmlId{4512}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2919}{\htmlId{4535}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2814}{\htmlId{4545}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2733}{\htmlId{4555}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{4562}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
      ⇀⦇ dereg c md ,DELEG⦈
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2919}{\htmlId{4604}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4612}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4614}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4616}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4618}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4620}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2814}{\htmlId{4624}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4632}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4634}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4636}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4638}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4640}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2733}{\htmlId{4644}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4649}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4651}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4653}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4655}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4657}{\htmlClass{Function Operator}{\text{ᶜ}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1869}{\htmlId{4667}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{4685}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{4688}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2210}{\htmlId{4689}{\htmlClass{InductiveConstructor}{\text{dereg}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4695}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3150}{\htmlId{4697}{\htmlClass{Generalizable}{\text{md}}}}\,\,\htmlId{4699}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{4701}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  DELEG-reg : let open PParams pp in
    ∙ c ∉ dom rwds
    ∙ d ≡ keyDeposit ⊎ d ≡ 0
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{4840}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{4845}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3246}{\htmlId{4853}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
        $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2919}{\htmlId{4878}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2814}{\htmlId{4888}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2733}{\htmlId{4898}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{4905}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$ ⇀⦇ reg c d ,DELEG⦈
        $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2919}{\htmlId{4940}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2814}{\htmlId{4950}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2733}{\htmlId{4960}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{4965}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4968}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{4970}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{4974}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4976}{\htmlClass{Field Operator}{\text{❵}}}}\,
        \\ \,\href{Ledger.Conway.Conformance.Certs.html#1869}{\htmlId{4988}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{5006}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{5009}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2829}{\htmlId{5010}{\htmlClass{InductiveConstructor}{\text{reg}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{5014}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3126}{\htmlId{5016}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{5017}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{5019}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

data _⊢_⇀⦇_,GOVCERT⦈_ : CertEnv → GState → DCert → GState → Type where
  GOVCERT-regdrep : ∀ {pp} → let open PParams pp in
    ∙ (d ≡ drepDeposit × c ∉ dom dReps) ⊎ (d ≡ 0 × c ∈ dom dReps)
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{5262}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#5120}{\htmlId{5266}{\htmlClass{Bound}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3356}{\htmlId{5271}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3033}{\htmlId{5276}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3257}{\htmlId{5284}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2768}{\htmlId{5299}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2862}{\htmlId{5307}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{5316}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
        ⇀⦇ regdrep c d an ,GOVCERT⦈
      $\begin{pmatrix} \,\href{Class.HasSingleton.html#288}{\htmlId{5366}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{5368}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{5372}{\htmlClass{Generalizable}{\text{e}}}}\, \,\href{Class.HasAdd.Core.html#162}{\htmlId{5374}{\htmlClass{Field Operator}{\text{+}}}}\, \,\href{Ledger.Conway.Specification.PParams.html#3513}{\htmlId{5376}{\htmlClass{Field}{\text{drepActivity}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5389}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{5391}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2768}{\htmlId{5394}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2862}{\htmlId{5402}{\htmlClass{Generalizable}{\text{ccKeys}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1869}{\htmlId{5417}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#5120}{\htmlId{5435}{\htmlClass{Bound}{\text{pp}}}}\, \,\htmlId{5438}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2348}{\htmlId{5439}{\htmlClass{InductiveConstructor}{\text{regdrep}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{5447}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3126}{\htmlId{5449}{\htmlClass{Generalizable}{\text{d}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3073}{\htmlId{5451}{\htmlClass{Generalizable}{\text{an}}}}\, \,\htmlId{5454}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{5456}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  GOVCERT-deregdrep :
    ∙ c ∈ dom dReps
    ∙ (DRepDeposit c , d) ∈ dep
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{5584}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{5588}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3356}{\htmlId{5593}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3033}{\htmlId{5598}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3257}{\htmlId{5606}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2768}{\htmlId{5615}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2862}{\htmlId{5623}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{5632}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
          ⇀⦇ deregdrep c d ,GOVCERT⦈
          $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2768}{\htmlId{5687}{\htmlClass{Generalizable}{\text{dReps}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{5693}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5695}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{5697}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5699}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{5701}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2862}{\htmlId{5705}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#1869}{\htmlId{5714}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{5732}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{5735}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2399}{\htmlId{5736}{\htmlClass{InductiveConstructor}{\text{deregdrep}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{5746}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3126}{\htmlId{5748}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{5749}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{5751}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  GOVCERT-ccreghot :
    ∙ (c , nothing) ∉ ccKeys
    ∙ c ∈ cc
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{5868}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{5872}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3356}{\htmlId{5877}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3033}{\htmlId{5882}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3257}{\htmlId{5890}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2768}{\htmlId{5899}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2862}{\htmlId{5907}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{5916}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
          ⇀⦇ ccreghot c mc ,GOVCERT⦈
          $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2768}{\htmlId{5971}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Class.HasSingleton.html#288}{\htmlId{5979}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{5981}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3210}{\htmlId{5985}{\htmlClass{Generalizable}{\text{mc}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5988}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{5990}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2862}{\htmlId{5993}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#1869}{\htmlId{6002}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{6020}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{6023}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2441}{\htmlId{6024}{\htmlClass{InductiveConstructor}{\text{ccreghot}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3180}{\htmlId{6033}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3210}{\htmlId{6035}{\htmlClass{Generalizable}{\text{mc}}}}\,\,\htmlId{6037}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3303}{\htmlId{6039}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

data _⊢_⇀⦇_,CERT⦈_ : CertEnv → CertState → DCert → CertState → Type where
  CERT-deleg :
    ∙ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{6143}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Specification.Certs.html#4141}{\htmlId{6148}{\htmlClass{Field}{\text{PState.pools}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{6161}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Class.IsSet.html#916}{\htmlId{6167}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{6171}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Conformance.Certs.html#850}{\htmlId{6172}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{6185}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{6188}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$ ⊢ stᵈ ⇀⦇ dCert ,DELEG⦈ stᵈ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{6267}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{6271}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3356}{\htmlId{6276}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3033}{\htmlId{6281}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3257}{\htmlId{6289}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3543}{\htmlId{6298}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{6304}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{6310}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3547}{\htmlId{6334}{\htmlClass{Generalizable}{\text{stᵈ'}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{6341}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{6347}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-pool :
    ∙ pp ⊢ stᵖ ⇀⦇ dCert ,POOL⦈ stᵖ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{6451}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{6455}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3356}{\htmlId{6460}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3033}{\htmlId{6465}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3257}{\htmlId{6473}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3543}{\htmlId{6482}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{6488}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{6494}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3543}{\htmlId{6518}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3587}{\htmlId{6524}{\htmlClass{Generalizable}{\text{stᵖ'}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{6531}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-vdel :
    ∙ Γ ⊢ stᵍ ⇀⦇ dCert ,GOVCERT⦈ stᵍ'
      ────────────────────────────────
      Γ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3543}{\htmlId{6641}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{6647}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{6653}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3543}{\htmlId{6677}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{6683}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3567}{\htmlId{6689}{\htmlClass{Generalizable}{\text{stᵍ'}}}}\, \end{pmatrix}$

data _⊢_⇀⦇_,PRE-CERT⦈_ : CertEnv → CertState → ⊤ → CertState → Type where

  CERT-pre :
    let open PParams pp
        refresh         = mapPartial (isGovVoterDRep ∘ voter) (fromList vs)
        refreshedDReps  = mapValueRestricted (const (e + drepActivity)) dReps refresh
        wdrlCreds       = mapˢ stake (dom wdrls)
    in
    ∙ filterˢ isKeyHash wdrlCreds ⊆ dom voteDelegs
    ∙ mapˢ (map₁ stake) (wdrls ˢ) ⊆ rewards ˢ
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{7171}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{7175}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3356}{\htmlId{7180}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3033}{\htmlId{7185}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3257}{\htmlId{7193}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2927}{\htmlId{7204}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2822}{\htmlId{7217}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2738}{\htmlId{7231}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3307}{\htmlId{7241}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{7250}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2768}{\htmlId{7258}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2869}{\htmlId{7266}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3312}{\htmlId{7278}{\htmlClass{Generalizable}{\text{gdep}}}}\, \end{pmatrix} \end{pmatrix}$
      ⇀⦇ _ ,PRE-CERT⦈
      $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2927}{\htmlId{7319}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2822}{\htmlId{7332}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#11988}{\htmlId{7346}{\htmlClass{Function}{\text{constMap}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#6979}{\htmlId{7355}{\htmlClass{Bound}{\text{wdrlCreds}}}}\, \,\htmlId{7365}{\htmlClass{Number}{\text{0}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{7367}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2738}{\htmlId{7370}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3307}{\htmlId{7380}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{7389}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#6893}{\htmlId{7397}{\htmlClass{Bound}{\text{refreshedDReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2869}{\htmlId{7414}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3312}{\htmlId{7426}{\htmlClass{Generalizable}{\text{gdep}}}}\, \end{pmatrix} \end{pmatrix}$

data _⊢_⇀⦇_,POST-CERT⦈_ : CertEnv → CertState → ⊤ → CertState → Type where

  CERT-post :
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3331}{\htmlId{7534}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3483}{\htmlId{7538}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3356}{\htmlId{7543}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3033}{\htmlId{7548}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3257}{\htmlId{7556}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$
      ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2927}{\htmlId{7573}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2822}{\htmlId{7586}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2738}{\htmlId{7600}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3307}{\htmlId{7610}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{7619}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{7625}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$
        ⇀⦇ _ ,POST-CERT⦈
        $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2927}{\htmlId{7668}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \,\href{Axiom.Set.Map.html#17775}{\htmlId{7679}{\htmlClass{Function Operator}{\text{∣\^{}}}}}\, \,\htmlId{7682}{\htmlClass{Symbol}{\text{(}}}\,\,\href{abstract-set-theory.FiniteSetTheory.html#519}{\htmlId{7683}{\htmlClass{Function}{\text{mapˢ}}}}\, \,\href{Ledger.Conway.Specification.Gov.Actions.html#3500}{\htmlId{7688}{\htmlClass{InductiveConstructor}{\text{vDelegCredential}}}}\, \,\htmlId{7705}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Class.IsSet.html#916}{\htmlId{7706}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{7710}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Conformance.Certs.html#850}{\htmlId{7711}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{7724}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{7727}{\htmlClass{Symbol}{\text{))}}}\, \,\href{Axiom.Set.html#9137}{\htmlId{7730}{\htmlClass{Function Operator}{\text{∪}}}}\, \,\href{Axiom.Set.html#5903}{\htmlId{7732}{\htmlClass{Function}{\text{fromList}}}}\, \,\htmlId{7741}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#3573}{\htmlId{7742}{\htmlClass{InductiveConstructor}{\text{vDelegNoConfidence}}}}\, \,\href{Agda.Builtin.List.html#199}{\htmlId{7761}{\htmlClass{InductiveConstructor Operator}{\text{∷}}}}\, \,\href{Ledger.Conway.Specification.Gov.Actions.html#3543}{\htmlId{7763}{\htmlClass{InductiveConstructor}{\text{vDelegAbstain}}}}\, \,\href{Agda.Builtin.List.html#199}{\htmlId{7777}{\htmlClass{InductiveConstructor Operator}{\text{∷}}}}\, \,\href{Agda.Builtin.List.html#184}{\htmlId{7779}{\htmlClass{InductiveConstructor}{\text{[]}}}}\,\,\htmlId{7781}{\htmlClass{Symbol}{\text{))}}}\,
          , \,\href{Ledger.Conway.Conformance.Certs.html#2822}{\htmlId{7796}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#2738}{\htmlId{7810}{\htmlClass{Generalizable}{\text{rewards}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3307}{\htmlId{7820}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} , \,\href{Ledger.Conway.Conformance.Certs.html#3583}{\htmlId{7829}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3563}{\htmlId{7835}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

_⊢_⇀⦇_,CERTS⦈_  : CertEnv → CertState  → List DCert  → CertState  → Type
_⊢_⇀⦇_,CERTS⦈_ = RunTraceAfterAndThen _⊢_⇀⦇_,PRE-CERT⦈_ _⊢_⇀⦇_,CERT⦈_ _⊢_⇀⦇_,POST-CERT⦈_