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 ≡ )
    ∙ mv ∈ mapˢ (just ∘ vDelegCredential) delegatees ∪
        fromList
          ( nothing
          ∷ just vDelegAbstain
          ∷ just vDelegNoConfidence
          ∷ []
          )
    ∙ mkh ∈ mapˢ just (dom pools) ∪ ❴ nothing ❵
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{4192}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3052}{\htmlId{4197}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3341}{\htmlId{4205}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3014}{\htmlId{4228}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2909}{\htmlId{4238}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2828}{\htmlId{4248}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{4255}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
      ⇀⦇ delegate c mv mkh d ,DELEG⦈
      $\begin{pmatrix} \,\href{Axiom.Set.Map.html#9262}{\htmlId{4306}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4319}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3605}{\htmlId{4321}{\htmlClass{Generalizable}{\text{mv}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3014}{\htmlId{4324}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#9262}{\htmlId{4334}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4347}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3510}{\htmlId{4349}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2909}{\htmlId{4353}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2828}{\htmlId{4363}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{4368}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4371}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4373}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{4377}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4379}{\htmlClass{Field Operator}{\text{❵}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1964}{\htmlId{4389}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{4407}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{4410}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2482}{\htmlId{4411}{\htmlClass{InductiveConstructor}{\text{delegate}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4420}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3605}{\htmlId{4422}{\htmlClass{Generalizable}{\text{mv}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3510}{\htmlId{4425}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3221}{\htmlId{4429}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{4430}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{4432}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  DELEG-dereg :
    ∙ (c , ) ∈ rwds
    ∙ (CredentialDeposit c , d) ∈ dep
    ∙ md ≡ nothing ⊎ md ≡ just d
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{4594}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3052}{\htmlId{4599}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3341}{\htmlId{4607}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3014}{\htmlId{4630}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2909}{\htmlId{4640}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2828}{\htmlId{4650}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{4657}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
      ⇀⦇ dereg c md ,DELEG⦈
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3014}{\htmlId{4699}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4707}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4709}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4711}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4713}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4715}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2909}{\htmlId{4719}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4727}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4729}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4731}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4733}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4735}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2828}{\htmlId{4739}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4744}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4746}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4748}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4750}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4752}{\htmlClass{Function Operator}{\text{ᶜ}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1964}{\htmlId{4762}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{4780}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{4783}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2555}{\htmlId{4784}{\htmlClass{InductiveConstructor}{\text{dereg}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{4790}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3245}{\htmlId{4792}{\htmlClass{Generalizable}{\text{md}}}}\,\,\htmlId{4794}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{4796}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  DELEG-reg : let open PParams pp in
    ∙ c ∉ dom rwds
    ∙ d ≡ keyDeposit ⊎ d ≡ 
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{4935}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3052}{\htmlId{4940}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3341}{\htmlId{4948}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
        $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3014}{\htmlId{4973}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2909}{\htmlId{4983}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2828}{\htmlId{4993}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{5000}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$ ⇀⦇ reg c d ,DELEG⦈
        $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3014}{\htmlId{5035}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2909}{\htmlId{5045}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2828}{\htmlId{5055}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{5060}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5063}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{5065}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{5069}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5071}{\htmlClass{Field Operator}{\text{❵}}}}\,
        \\ \,\href{Ledger.Conway.Conformance.Certs.html#1964}{\htmlId{5083}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{5101}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{5104}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#3190}{\htmlId{5105}{\htmlClass{InductiveConstructor}{\text{reg}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{5109}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3221}{\htmlId{5111}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{5112}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{5114}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

data _⊢_⇀⦇_,GOVCERT⦈_ : CertEnv → GState → DCert → GState → Type where
  GOVCERT-regdrep : ∀ {pp} → let open PParams pp in
    ∙ (d ≡ drepDeposit × c ∉ dom dReps) ⊎ (d ≡  × c ∈ dom dReps)
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{5357}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#5215}{\htmlId{5361}{\htmlClass{Bound}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3451}{\htmlId{5366}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3128}{\htmlId{5371}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3352}{\htmlId{5379}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2863}{\htmlId{5394}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{5402}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{5411}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
        ⇀⦇ regdrep c d an ,GOVCERT⦈
      $\begin{pmatrix} \,\href{Class.HasSingleton.html#288}{\htmlId{5461}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{5463}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{5467}{\htmlClass{Generalizable}{\text{e}}}}\, \,\href{Class.HasAdd.Core.html#162}{\htmlId{5469}{\htmlClass{Field Operator}{\text{+}}}}\, \,\href{Ledger.Conway.Specification.PParams.html#7504}{\htmlId{5471}{\htmlClass{Field}{\text{drepActivity}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5484}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{5486}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2863}{\htmlId{5489}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{5497}{\htmlClass{Generalizable}{\text{ccKeys}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1964}{\htmlId{5512}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#5215}{\htmlId{5530}{\htmlClass{Bound}{\text{pp}}}}\, \,\htmlId{5533}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2693}{\htmlId{5534}{\htmlClass{InductiveConstructor}{\text{regdrep}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{5542}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3221}{\htmlId{5544}{\htmlClass{Generalizable}{\text{d}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3168}{\htmlId{5546}{\htmlClass{Generalizable}{\text{an}}}}\, \,\htmlId{5549}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{5551}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  GOVCERT-deregdrep :
    ∙ c ∈ dom dReps
    ∙ (DRepDeposit c , d) ∈ dep
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{5679}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{5683}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3451}{\htmlId{5688}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3128}{\htmlId{5693}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3352}{\htmlId{5701}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2863}{\htmlId{5710}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{5718}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{5727}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
          ⇀⦇ deregdrep c d ,GOVCERT⦈
          $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2863}{\htmlId{5782}{\htmlClass{Generalizable}{\text{dReps}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{5788}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5790}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{5792}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5794}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{5796}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{5800}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#1964}{\htmlId{5809}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{5827}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{5830}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2744}{\htmlId{5831}{\htmlClass{InductiveConstructor}{\text{deregdrep}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{5841}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3221}{\htmlId{5843}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{5844}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{5846}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  GOVCERT-ccreghot :
    ∙ (c , nothing) ∉ ccKeys
    ∙ c ∈ cc
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{5963}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{5967}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3451}{\htmlId{5972}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3128}{\htmlId{5977}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3352}{\htmlId{5985}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2863}{\htmlId{5994}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{6002}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{6011}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
          ⇀⦇ ccreghot c mc ,GOVCERT⦈
          $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2863}{\htmlId{6066}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Class.HasSingleton.html#288}{\htmlId{6074}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{6076}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3305}{\htmlId{6080}{\htmlClass{Generalizable}{\text{mc}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{6083}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{6085}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2957}{\htmlId{6088}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#1964}{\htmlId{6097}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{6115}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{6118}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2786}{\htmlId{6119}{\htmlClass{InductiveConstructor}{\text{ccreghot}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3275}{\htmlId{6128}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3305}{\htmlId{6130}{\htmlClass{Generalizable}{\text{mc}}}}\,\,\htmlId{6132}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3398}{\htmlId{6134}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

data _⊢_⇀⦇_,CERT⦈_ : CertEnv → CertState → DCert → CertState → Type where
  CERT-deleg :
    ∙ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{6238}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Specification.Certs.html#4604}{\htmlId{6243}{\htmlClass{Field}{\text{PState.pools}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{6256}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Class.IsSet.html#916}{\htmlId{6262}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{6266}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Conformance.Certs.html#945}{\htmlId{6267}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{6280}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{6283}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$ ⊢ stᵈ ⇀⦇ dCert ,DELEG⦈ stᵈ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{6362}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{6366}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3451}{\htmlId{6371}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3128}{\htmlId{6376}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3352}{\htmlId{6384}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3638}{\htmlId{6393}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{6399}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{6405}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3642}{\htmlId{6429}{\htmlClass{Generalizable}{\text{stᵈ'}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{6436}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{6442}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-pool :
    ∙ pp ⊢ stᵖ ⇀⦇ dCert ,POOL⦈ stᵖ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{6546}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{6550}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3451}{\htmlId{6555}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3128}{\htmlId{6560}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3352}{\htmlId{6568}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3638}{\htmlId{6577}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{6583}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{6589}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3638}{\htmlId{6613}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3682}{\htmlId{6619}{\htmlClass{Generalizable}{\text{stᵖ'}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{6626}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-vdel :
    ∙ Γ ⊢ stᵍ ⇀⦇ dCert ,GOVCERT⦈ stᵍ'
      ────────────────────────────────
      Γ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3638}{\htmlId{6736}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{6742}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{6748}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3638}{\htmlId{6772}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{6778}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3662}{\htmlId{6784}{\htmlClass{Generalizable}{\text{stᵍ'}}}}\, \end{pmatrix}$

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
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{7266}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{7270}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3451}{\htmlId{7275}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3128}{\htmlId{7280}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3352}{\htmlId{7288}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3022}{\htmlId{7299}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2917}{\htmlId{7312}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2833}{\htmlId{7326}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3402}{\htmlId{7336}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{7345}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2863}{\htmlId{7353}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2964}{\htmlId{7361}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3407}{\htmlId{7373}{\htmlClass{Generalizable}{\text{gdep}}}}\, \end{pmatrix} \end{pmatrix}$
      ⇀⦇ _ ,PRE-CERT⦈
      $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3022}{\htmlId{7414}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2917}{\htmlId{7427}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#11988}{\htmlId{7441}{\htmlClass{Function}{\text{constMap}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#7074}{\htmlId{7450}{\htmlClass{Bound}{\text{wdrlCreds}}}}\, \,\htmlId{7460}{\htmlClass{Number}{\text{0}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{7462}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2833}{\htmlId{7465}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3402}{\htmlId{7475}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{7484}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#6988}{\htmlId{7492}{\htmlClass{Bound}{\text{refreshedDReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2964}{\htmlId{7509}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3407}{\htmlId{7521}{\htmlClass{Generalizable}{\text{gdep}}}}\, \end{pmatrix} \end{pmatrix}$

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

  CERT-post :
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3426}{\htmlId{7629}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3578}{\htmlId{7633}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3451}{\htmlId{7638}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3128}{\htmlId{7643}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3352}{\htmlId{7651}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$
      ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3022}{\htmlId{7668}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2917}{\htmlId{7681}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2833}{\htmlId{7695}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3402}{\htmlId{7705}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{7714}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{7720}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$
        ⇀⦇ _ ,POST-CERT⦈
        $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3022}{\htmlId{7763}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \,\href{Axiom.Set.Map.html#17775}{\htmlId{7774}{\htmlClass{Function Operator}{\text{∣\^{}}}}}\, \,\htmlId{7777}{\htmlClass{Symbol}{\text{(}}}\,\,\href{abstract-set-theory.FiniteSetTheory.html#519}{\htmlId{7778}{\htmlClass{Function}{\text{mapˢ}}}}\, \,\href{Ledger.Conway.Specification.Gov.Actions.html#8396}{\htmlId{7783}{\htmlClass{InductiveConstructor}{\text{vDelegCredential}}}}\, \,\htmlId{7800}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Class.IsSet.html#916}{\htmlId{7801}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{7805}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Conformance.Certs.html#945}{\htmlId{7806}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{7819}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{7822}{\htmlClass{Symbol}{\text{))}}}\, \,\href{Axiom.Set.html#9137}{\htmlId{7825}{\htmlClass{Function Operator}{\text{∪}}}}\, \,\href{Axiom.Set.html#5903}{\htmlId{7827}{\htmlClass{Function}{\text{fromList}}}}\, \,\htmlId{7836}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#8469}{\htmlId{7837}{\htmlClass{InductiveConstructor}{\text{vDelegNoConfidence}}}}\, \,\href{Agda.Builtin.List.html#199}{\htmlId{7856}{\htmlClass{InductiveConstructor Operator}{\text{∷}}}}\, \,\href{Ledger.Conway.Specification.Gov.Actions.html#8439}{\htmlId{7858}{\htmlClass{InductiveConstructor}{\text{vDelegAbstain}}}}\, \,\href{Agda.Builtin.List.html#199}{\htmlId{7872}{\htmlClass{InductiveConstructor Operator}{\text{∷}}}}\, \,\href{Agda.Builtin.List.html#184}{\htmlId{7874}{\htmlClass{InductiveConstructor}{\text{[]}}}}\,\,\htmlId{7876}{\htmlClass{Symbol}{\text{))}}}\,
          , \,\href{Ledger.Conway.Conformance.Certs.html#2917}{\htmlId{7891}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#2833}{\htmlId{7905}{\htmlClass{Generalizable}{\text{rewards}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3402}{\htmlId{7915}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} , \,\href{Ledger.Conway.Conformance.Certs.html#3678}{\htmlId{7924}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3658}{\htmlId{7930}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

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