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 ❵
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{4189}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3049}{\htmlId{4194}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3338}{\htmlId{4202}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3011}{\htmlId{4225}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2906}{\htmlId{4235}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2825}{\htmlId{4245}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{4252}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
      ⇀⦇ delegate c mv mkh d ,DELEG⦈
      $\begin{pmatrix} \,\href{Axiom.Set.Map.html#9262}{\htmlId{4303}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4316}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3602}{\htmlId{4318}{\htmlClass{Generalizable}{\text{mv}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3011}{\htmlId{4321}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#9262}{\htmlId{4331}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4344}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3507}{\htmlId{4346}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2906}{\htmlId{4350}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2825}{\htmlId{4360}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{4365}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4368}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4370}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{4374}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4376}{\htmlClass{Field Operator}{\text{❵}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1961}{\htmlId{4386}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{4404}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{4407}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2482}{\htmlId{4408}{\htmlClass{InductiveConstructor}{\text{delegate}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4417}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3602}{\htmlId{4419}{\htmlClass{Generalizable}{\text{mv}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3507}{\htmlId{4422}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3218}{\htmlId{4426}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{4427}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{4429}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  DELEG-dereg :
    ∙ (c , ) ∈ rwds
    ∙ (CredentialDeposit c , d) ∈ dep
    ∙ md ≡ nothing ⊎ md ≡ just d
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{4591}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3049}{\htmlId{4596}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3338}{\htmlId{4604}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3011}{\htmlId{4627}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2906}{\htmlId{4637}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2825}{\htmlId{4647}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{4654}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
      ⇀⦇ dereg c md ,DELEG⦈
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3011}{\htmlId{4696}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4704}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4706}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4708}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4710}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4712}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2906}{\htmlId{4716}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4724}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4726}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4728}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4730}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4732}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2825}{\htmlId{4736}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4741}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4743}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4745}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{4747}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{4749}{\htmlClass{Function Operator}{\text{ᶜ}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1961}{\htmlId{4759}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{4777}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{4780}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2555}{\htmlId{4781}{\htmlClass{InductiveConstructor}{\text{dereg}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{4787}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3242}{\htmlId{4789}{\htmlClass{Generalizable}{\text{md}}}}\,\,\htmlId{4791}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{4793}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  DELEG-reg : let open PParams pp in
    ∙ c ∉ dom rwds
    ∙ d ≡ keyDeposit ⊎ d ≡ 
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{4932}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3049}{\htmlId{4937}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3338}{\htmlId{4945}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢
        $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3011}{\htmlId{4970}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2906}{\htmlId{4980}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2825}{\htmlId{4990}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{4997}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$ ⇀⦇ reg c d ,DELEG⦈
        $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3011}{\htmlId{5032}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2906}{\htmlId{5042}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2825}{\htmlId{5052}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{5057}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5060}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{5062}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{5066}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5068}{\htmlClass{Field Operator}{\text{❵}}}}\,
        \\ \,\href{Ledger.Conway.Conformance.Certs.html#1961}{\htmlId{5080}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{5098}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{5101}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#3190}{\htmlId{5102}{\htmlClass{InductiveConstructor}{\text{reg}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{5106}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3218}{\htmlId{5108}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{5109}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{5111}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

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)
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{5354}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#5212}{\htmlId{5358}{\htmlClass{Bound}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3448}{\htmlId{5363}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3125}{\htmlId{5368}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3349}{\htmlId{5376}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2860}{\htmlId{5391}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2954}{\htmlId{5399}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{5408}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
        ⇀⦇ regdrep c d an ,GOVCERT⦈
      $\begin{pmatrix} \,\href{Class.HasSingleton.html#288}{\htmlId{5458}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{5460}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{5464}{\htmlClass{Generalizable}{\text{e}}}}\, \,\href{Class.HasAdd.Core.html#162}{\htmlId{5466}{\htmlClass{Field Operator}{\text{+}}}}\, \,\href{Ledger.Conway.Specification.PParams.html#7468}{\htmlId{5468}{\htmlClass{Field}{\text{drepActivity}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5481}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{5483}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2860}{\htmlId{5486}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2954}{\htmlId{5494}{\htmlClass{Generalizable}{\text{ccKeys}}}}\,
      \\ \,\href{Ledger.Conway.Conformance.Certs.html#1961}{\htmlId{5509}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#5212}{\htmlId{5527}{\htmlClass{Bound}{\text{pp}}}}\, \,\htmlId{5530}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2693}{\htmlId{5531}{\htmlClass{InductiveConstructor}{\text{regdrep}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{5539}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3218}{\htmlId{5541}{\htmlClass{Generalizable}{\text{d}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3165}{\htmlId{5543}{\htmlClass{Generalizable}{\text{an}}}}\, \,\htmlId{5546}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{5548}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  GOVCERT-deregdrep :
    ∙ c ∈ dom dReps
    ∙ (DRepDeposit c , d) ∈ dep
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{5676}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{5680}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3448}{\htmlId{5685}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3125}{\htmlId{5690}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3349}{\htmlId{5698}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2860}{\htmlId{5707}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2954}{\htmlId{5715}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{5724}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
          ⇀⦇ deregdrep c d ,GOVCERT⦈
          $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2860}{\htmlId{5779}{\htmlClass{Generalizable}{\text{dReps}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{5785}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5787}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{5789}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{5791}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{5793}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2954}{\htmlId{5797}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#1961}{\htmlId{5806}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{5824}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{5827}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2744}{\htmlId{5828}{\htmlClass{InductiveConstructor}{\text{deregdrep}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{5838}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3218}{\htmlId{5840}{\htmlClass{Generalizable}{\text{d}}}}\,\,\htmlId{5841}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{5843}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

  GOVCERT-ccreghot :
    ∙ (c , nothing) ∉ ccKeys
    ∙ c ∈ cc
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{5960}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{5964}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3448}{\htmlId{5969}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3125}{\htmlId{5974}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3349}{\htmlId{5982}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2860}{\htmlId{5991}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2954}{\htmlId{5999}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{6008}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$
          ⇀⦇ ccreghot c mc ,GOVCERT⦈
          $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2860}{\htmlId{6063}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Class.HasSingleton.html#288}{\htmlId{6071}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{6073}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3302}{\htmlId{6077}{\htmlClass{Generalizable}{\text{mc}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{6080}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{6082}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2954}{\htmlId{6085}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#1961}{\htmlId{6094}{\htmlClass{Function}{\text{updateCertDeposit}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{6112}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{6115}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Certs.html#2786}{\htmlId{6116}{\htmlClass{InductiveConstructor}{\text{ccreghot}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3272}{\htmlId{6125}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3302}{\htmlId{6127}{\htmlClass{Generalizable}{\text{mc}}}}\,\,\htmlId{6129}{\htmlClass{Symbol}{\text{)}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3395}{\htmlId{6131}{\htmlClass{Generalizable}{\text{dep}}}}\, \end{pmatrix}$

data _⊢_⇀⦇_,CERT⦈_ : CertEnv → CertState → DCert → CertState → Type where
  CERT-deleg :
    ∙ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{6235}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Specification.Certs.html#4404}{\htmlId{6240}{\htmlClass{Field}{\text{PState.pools}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{6253}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Class.IsSet.html#916}{\htmlId{6259}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{6263}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Conformance.Certs.html#942}{\htmlId{6264}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{6277}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{6280}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$ ⊢ stᵈ ⇀⦇ dCert ,DELEG⦈ stᵈ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{6359}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{6363}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3448}{\htmlId{6368}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3125}{\htmlId{6373}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3349}{\htmlId{6381}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3635}{\htmlId{6390}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{6396}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{6402}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3639}{\htmlId{6426}{\htmlClass{Generalizable}{\text{stᵈ'}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{6433}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{6439}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-pool :
    ∙ pp ⊢ stᵖ ⇀⦇ dCert ,POOL⦈ stᵖ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{6543}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{6547}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3448}{\htmlId{6552}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3125}{\htmlId{6557}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3349}{\htmlId{6565}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3635}{\htmlId{6574}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{6580}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{6586}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3635}{\htmlId{6610}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3679}{\htmlId{6616}{\htmlClass{Generalizable}{\text{stᵖ'}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{6623}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-vdel :
    ∙ Γ ⊢ stᵍ ⇀⦇ dCert ,GOVCERT⦈ stᵍ'
      ────────────────────────────────
      Γ ⊢ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3635}{\htmlId{6733}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{6739}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{6745}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3635}{\htmlId{6769}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{6775}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3659}{\htmlId{6781}{\htmlClass{Generalizable}{\text{stᵍ'}}}}\, \end{pmatrix}$

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
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{7263}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{7267}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3448}{\htmlId{7272}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3125}{\htmlId{7277}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3349}{\htmlId{7285}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3019}{\htmlId{7296}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2914}{\htmlId{7309}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2830}{\htmlId{7323}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3399}{\htmlId{7333}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{7342}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#2860}{\htmlId{7350}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2961}{\htmlId{7358}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3404}{\htmlId{7370}{\htmlClass{Generalizable}{\text{gdep}}}}\, \end{pmatrix} \end{pmatrix}$
      ⇀⦇ _ ,PRE-CERT⦈
      $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3019}{\htmlId{7411}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2914}{\htmlId{7424}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#11988}{\htmlId{7438}{\htmlClass{Function}{\text{constMap}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#7071}{\htmlId{7447}{\htmlClass{Bound}{\text{wdrlCreds}}}}\, \,\htmlId{7457}{\htmlClass{Number}{\text{0}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{7459}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#2830}{\htmlId{7462}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3399}{\htmlId{7472}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{7481}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#6985}{\htmlId{7489}{\htmlClass{Bound}{\text{refreshedDReps}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2961}{\htmlId{7506}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3404}{\htmlId{7518}{\htmlClass{Generalizable}{\text{gdep}}}}\, \end{pmatrix} \end{pmatrix}$

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

  CERT-post :
      $\begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3423}{\htmlId{7626}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3575}{\htmlId{7630}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3448}{\htmlId{7635}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3125}{\htmlId{7640}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3349}{\htmlId{7648}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$
      ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3019}{\htmlId{7665}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2914}{\htmlId{7678}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#2830}{\htmlId{7692}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3399}{\htmlId{7702}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} \\ \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{7711}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{7717}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$
        ⇀⦇ _ ,POST-CERT⦈
        $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Conway.Conformance.Certs.html#3019}{\htmlId{7760}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \,\href{Axiom.Set.Map.html#17775}{\htmlId{7771}{\htmlClass{Function Operator}{\text{∣\^{}}}}}\, \,\htmlId{7774}{\htmlClass{Symbol}{\text{(}}}\,\,\href{abstract-set-theory.FiniteSetTheory.html#519}{\htmlId{7775}{\htmlClass{Function}{\text{mapˢ}}}}\, \,\href{Ledger.Conway.Specification.Gov.Actions.html#6846}{\htmlId{7780}{\htmlClass{InductiveConstructor}{\text{vDelegCredential}}}}\, \,\htmlId{7797}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Class.IsSet.html#916}{\htmlId{7798}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{7802}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Conformance.Certs.html#942}{\htmlId{7803}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{7816}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{7819}{\htmlClass{Symbol}{\text{))}}}\, \,\href{Axiom.Set.html#9137}{\htmlId{7822}{\htmlClass{Function Operator}{\text{∪}}}}\, \,\href{Axiom.Set.html#5903}{\htmlId{7824}{\htmlClass{Function}{\text{fromList}}}}\, \,\htmlId{7833}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Conway.Specification.Gov.Actions.html#6919}{\htmlId{7834}{\htmlClass{InductiveConstructor}{\text{vDelegNoConfidence}}}}\, \,\href{Agda.Builtin.List.html#199}{\htmlId{7853}{\htmlClass{InductiveConstructor Operator}{\text{∷}}}}\, \,\href{Ledger.Conway.Specification.Gov.Actions.html#6889}{\htmlId{7855}{\htmlClass{InductiveConstructor}{\text{vDelegAbstain}}}}\, \,\href{Agda.Builtin.List.html#199}{\htmlId{7869}{\htmlClass{InductiveConstructor Operator}{\text{∷}}}}\, \,\href{Agda.Builtin.List.html#184}{\htmlId{7871}{\htmlClass{InductiveConstructor}{\text{[]}}}}\,\,\htmlId{7873}{\htmlClass{Symbol}{\text{))}}}\,
          , \,\href{Ledger.Conway.Conformance.Certs.html#2914}{\htmlId{7888}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#2830}{\htmlId{7902}{\htmlClass{Generalizable}{\text{rewards}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3399}{\htmlId{7912}{\htmlClass{Generalizable}{\text{ddep}}}}\, \end{pmatrix} , \,\href{Ledger.Conway.Conformance.Certs.html#3675}{\htmlId{7921}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, , \,\href{Ledger.Conway.Conformance.Certs.html#3655}{\htmlId{7927}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

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