Certificates

{-# OPTIONS --safe #-}

open import Ledger.Dijkstra.Specification.Gov.Base using (GovStructure)

module Ledger.Dijkstra.Specification.Certs
  (gs : GovStructure) (open GovStructure gs) where

open import Ledger.Prelude renaming (filterˢ to filter)
open import Ledger.Prelude.Numeric.UnitInterval
open import Ledger.Dijkstra.Specification.Gov.Actions gs hiding (yes; no)
open RewardAddress
open PParams

record StakePoolParams : Type where
  field
    owners          : ℙ KeyHash
    cost            : Coin
    margin          : UnitInterval
    pledge          : Coin
    rewardAccount   : Credential

-- Miscellaneous Type Aliases

CCHotKeys : Type
CCHotKeys = Credential ⇀ Maybe Credential

PoolEnv : Type
PoolEnv = PParams

Pools : Type
Pools = KeyHash ⇀ StakePoolParams

Retiring : Type
Retiring = KeyHash ⇀ Epoch

Rewards : Type
Rewards = Credential ⇀ Coin

Stake : Type
Stake = Credential ⇀ Coin

StakeDelegs : Type
StakeDelegs = Credential ⇀ KeyHash

-- Delegation Definitions
data DCert : Type where
  delegate    : Credential → Maybe VDeleg → Maybe KeyHash → Coin → DCert
  dereg       : Credential → Maybe Coin → DCert
  regpool     : KeyHash → StakePoolParams → DCert
  retirepool  : KeyHash → Epoch → DCert
  regdrep     : Credential → Coin → Anchor → DCert
  deregdrep   : Credential → Coin → DCert
  ccreghot    : Credential → Maybe Credential → DCert

cwitness : DCert → Maybe Credential
cwitness (delegate c _ _ _)  = just c
cwitness (dereg c _)         = just c
cwitness (regpool kh _)      = just $ KeyHashObj kh
cwitness (retirepool kh _)   = just $ KeyHashObj kh
cwitness (regdrep c _ _)     = just c
cwitness (deregdrep c _)     = just c
cwitness (ccreghot c _)      = just c

-- Certification Types
record CertEnv : Type where
  field
    epoch     : Epoch
    pp        : PParams
    votes     : List GovVote
    wdrls     : Withdrawals
    coldCreds : ℙ Credential

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

record PState : Type where
  field
    pools     : Pools
    fPools    : Pools
    retiring  : KeyHash ⇀ Epoch
    deposits  : KeyHash ⇀ Coin

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

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

record DelegEnv : Type where
  field
    pparams       : PParams
    pools         : Pools
    delegatees    : ℙ Credential

record HasDeposits (A : Type) {K : Type} : Type where
  field DepositsOf : A → K ⇀ Coin
open HasDeposits ⦃...⦄ public

record HasCCHotKeys {a} (A : Type a) : Type a where
  field CCHotKeysOf : A → CCHotKeys
open HasCCHotKeys ⦃...⦄ public

record HasPools {a} (A : Type a) : Type a where
  field PoolsOf : A → Pools
open HasPools ⦃...⦄ public

record HasRetiring {a} (A : Type a) : Type a where
  field RetiringOf : A → Retiring
open HasRetiring ⦃...⦄ public

record HasRewards {a} (A : Type a) : Type a where
  field RewardsOf : A → Rewards
open HasRewards ⦃...⦄ public

record HasStake {a} (A : Type a) : Type a where
  field StakeOf : A -> Stake
open HasStake ⦃...⦄ public

record HasStakeDelegs {a} (A : Type a) : Type a where
  field StakeDelegsOf : A -> StakeDelegs
open HasStakeDelegs ⦃...⦄ public

record HasDState {a} (A : Type a) : Type a where
  field DStateOf : A → DState
open HasDState ⦃...⦄ public

record HasPState {a} (A : Type a) : Type a where
  field PStateOf : A → PState
open HasPState ⦃...⦄ public

record HasGState {a} (A : Type a) : Type a where
  field GStateOf : A → GState
open HasGState ⦃...⦄ public

record HasCertState {a} (A : Type a) : Type a where
  field CertStateOf : A → CertState
open HasCertState ⦃...⦄ public

instance
  HasPParams-CertEnv : HasPParams CertEnv
  HasPParams-CertEnv .PParamsOf = CertEnv.pp

  HasWithdrawals-CertEnv : HasWithdrawals CertEnv
  HasWithdrawals-CertEnv .WithdrawalsOf = CertEnv.wdrls

  HasVoteDelegs-DState : HasVoteDelegs DState
  HasVoteDelegs-DState .VoteDelegsOf = DState.voteDelegs

  HasStakeDelegs-DState : HasStakeDelegs DState
  HasStakeDelegs-DState .StakeDelegsOf = DState.stakeDelegs

  HasRewards-DState : HasRewards DState
  HasRewards-DState .RewardsOf = DState.rewards

  HasDeposits-DState : HasDeposits DState
  HasDeposits-DState .DepositsOf = DState.deposits

  HasPools-PState : HasPools PState
  HasPools-PState .PoolsOf = PState.pools

  HasDeposits-PState : HasDeposits PState
  HasDeposits-PState .DepositsOf = PState.deposits

  HasRetiring-PState : HasRetiring PState
  HasRetiring-PState .RetiringOf = PState.retiring

  HasDReps-GState : HasDReps GState
  HasDReps-GState .DRepsOf = GState.dreps

  HasCCHotKeys-GState : HasCCHotKeys GState
  HasCCHotKeys-GState .CCHotKeysOf = GState.ccHotKeys

  HasDeposits-GState : HasDeposits GState
  HasDeposits-GState .DepositsOf = GState.deposits

  HasDState-CertState : HasDState CertState
  HasDState-CertState .DStateOf = CertState.dState

  HasPState-CertState : HasPState CertState
  HasPState-CertState .PStateOf = CertState.pState

  HasGState-CertState : HasGState CertState
  HasGState-CertState .GStateOf = CertState.gState

  HasRewards-CertState : HasRewards CertState
  HasRewards-CertState .RewardsOf = RewardsOf ∘ DStateOf

  HasDReps-CertState : HasDReps CertState
  HasDReps-CertState .DRepsOf = DRepsOf ∘ GStateOf

  HasCCHotKeys-CertState : HasCCHotKeys CertState
  HasCCHotKeys-CertState .CCHotKeysOf = CCHotKeysOf ∘ GStateOf

  HasPools-CertState : HasPools CertState
  HasPools-CertState .PoolsOf = PoolsOf ∘ PStateOf

  HasVoteDelegs-CertState : HasVoteDelegs CertState
  HasVoteDelegs-CertState .VoteDelegsOf = VoteDelegsOf ∘ DStateOf

  HasStakeDelegs-CertState : HasStakeDelegs CertState
  HasStakeDelegs-CertState .StakeDelegsOf = StakeDelegsOf ∘ DStateOf

  unquoteDecl HasCast-CertEnv HasCast-DState HasCast-PState HasCast-GState HasCast-CertState HasCast-DelegEnv = derive-HasCast
    (   (quote CertEnv , HasCast-CertEnv)
    ∷   (quote DState , HasCast-DState)
    ∷   (quote PState , HasCast-PState)
    ∷   (quote GState , HasCast-GState)
    ∷   (quote CertState , HasCast-CertState)
    ∷ [ (quote DelegEnv , HasCast-DelegEnv) ])


private variable
  rwds rewards           : Rewards
  dReps                  : DReps
  sDelegs stakeDelegs    : StakeDelegs
  ccKeys ccHotKeys       : CCHotKeys
  vDelegs voteDelegs     : VoteDelegs
  pools fPools           : Pools
  retiring               : Retiring
  wdrls                  : Withdrawals
  A                      : Type
  deposits deposits'     : A ⇀ Coin

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

  stᵈ stᵈ' : DState
  stᵍ stᵍ' : GState
  stᵖ stᵖ' : PState
  cc : ℙ Credential

rewardsBalance : DState → Coin
rewardsBalance ds = ∑[ x ← RewardsOf ds ] x

instance
  HasCoin-CertState : HasCoin CertState
  HasCoin-CertState .getCoin = rewardsBalance ∘ DStateOf

-- Auxiliary DELEG transition system --
data _⊢_⇀⦇_,DELEG⦈_ : DelegEnv → DState → DCert → DState → Type where

  DELEG-delegate :
    ∙ (c ∉ dom rwds → d ≡ pp .keyDeposit)
    ∙ (c ∈ dom rwds → d ≡ )
    ∙ mvd ∈ mapˢ (just ∘ vDelegCredential) delegatees ∪
            fromList ( nothing ∷ just vDelegAbstain ∷ just vDelegNoConfidence ∷ [] )
    ∙ mkh ∈ mapˢ just (dom pools) ∪ ❴ nothing ❵
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{8036}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{8041}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7045}{\htmlId{8049}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6675}{\htmlId{8066}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{8076}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6531}{\htmlId{8086}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{8093}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ delegate c mvd mkh d ,DELEG⦈ $\begin{pmatrix} \,\href{Axiom.Set.Map.html#9262}{\htmlId{8138}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8151}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7257}{\htmlId{8153}{\htmlClass{Generalizable}{\text{mvd}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6675}{\htmlId{8157}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#9262}{\htmlId{8167}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8180}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7171}{\htmlId{8182}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{8186}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6531}{\htmlId{8196}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{8201}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8204}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8206}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{8210}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8212}{\htmlClass{Field Operator}{\text{❵}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{8216}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.Dec.html#2149}{\htmlId{8225}{\htmlClass{Function Operator}{\text{∪⁺}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8228}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8230}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#6937}{\htmlId{8234}{\htmlClass{Generalizable}{\text{d}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8236}{\htmlClass{Field Operator}{\text{❵}}}}\, \end{pmatrix}$

  DELEG-dereg :
    ∙ (c , ) ∈ rwds
    ∙ (c , d) ∈ deposits
    ∙ md ≡ nothing ⊎ md ≡ just d
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{8383}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{8388}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7045}{\htmlId{8396}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6675}{\htmlId{8413}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{8423}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6531}{\htmlId{8433}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{8440}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ dereg c md ,DELEG⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6675}{\htmlId{8475}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8483}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8485}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8487}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8489}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8491}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{8495}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8503}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8505}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8507}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8509}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8511}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6531}{\htmlId{8515}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8520}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8522}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8524}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8526}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8528}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{8532}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8541}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8543}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{8545}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8547}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{8549}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \end{pmatrix}$


isPoolRegistered : Pools -> KeyHash -> Maybe StakePoolParams
isPoolRegistered ps kh = lookupᵐ? ps kh

-- Auxiliary POOL transition system --
data _⊢_⇀⦇_,POOL⦈_ : PoolEnv → PState → DCert → PState → Type where

  POOL-reg :
    ∙ Is-nothing (isPoolRegistered pools kh)
    ────────────────────────────────
    pp ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{8871}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6719}{\htmlId{8888}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6746}{\htmlId{8906}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{8926}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$ ⇀⦇ regpool kh poolParams ,POOL⦈ $\begin{pmatrix}
           \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{8991}{\htmlClass{Generalizable}{\text{pools}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{8997}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9000}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7147}{\htmlId{9002}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7201}{\htmlId{9007}{\htmlClass{Generalizable}{\text{poolParams}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9018}{\htmlClass{Field Operator}{\text{❵}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6719}{\htmlId{9031}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6746}{\htmlId{9049}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{9069}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{9078}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9081}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7147}{\htmlId{9083}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{9088}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{9091}{\htmlClass{Symbol}{\text{.}}}\,\,\href{Ledger.Dijkstra.Specification.PParams.html#3137}{\htmlId{9092}{\htmlClass{Field}{\text{poolDeposit}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9104}{\htmlClass{Field Operator}{\text{❵}}}}\,
         \end{pmatrix}$

  POOL-rereg :
    ∙ Is-just (isPoolRegistered pools kh)
    ────────────────────────────────
    pp ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{9223}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6719}{\htmlId{9240}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6746}{\htmlId{9258}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{9278}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$ ⇀⦇ regpool kh poolParams ,POOL⦈ $\begin{pmatrix}
           \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{9343}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Class.HasSingleton.html#288}{\htmlId{9360}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7147}{\htmlId{9362}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7201}{\htmlId{9367}{\htmlClass{Generalizable}{\text{poolParams}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9378}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{9380}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6719}{\htmlId{9383}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6746}{\htmlId{9401}{\htmlClass{Generalizable}{\text{retiring}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9410}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9412}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7147}{\htmlId{9414}{\htmlClass{Generalizable}{\text{kh}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9417}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9419}{\htmlClass{Function Operator}{\text{ᶜ}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{9432}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$

  POOL-retirepool :
    ────────────────────────────────
    pp ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{9521}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6719}{\htmlId{9538}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6746}{\htmlId{9556}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{9576}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$ ⇀⦇ retirepool kh e ,POOL⦈ $\begin{pmatrix}
           \,\href{Ledger.Dijkstra.Specification.Certs.html#6713}{\htmlId{9635}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6719}{\htmlId{9652}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Class.HasSingleton.html#288}{\htmlId{9670}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7147}{\htmlId{9672}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{9677}{\htmlClass{Generalizable}{\text{e}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9679}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{9681}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6746}{\htmlId{9684}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{9704}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$


-- Auxiliary GOVCERT transition system --
data _⊢_⇀⦇_,GOVCERT⦈_ : CertEnv → GState → DCert → GState → Type where

  GOVCERT-regdrep :
    ∙ (d ≡ pp .drepDeposit × c ∉ dom dReps) ⊎ (d ≡  × c ∈ dom dReps)
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{9977}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{9981}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7118}{\htmlId{9986}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6782}{\htmlId{9991}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7347}{\htmlId{9999}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6566}{\htmlId{10008}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6638}{\htmlId{10016}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{10025}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ regdrep c d an ,GOVCERT⦈ $\begin{pmatrix} \,\href{Class.HasSingleton.html#288}{\htmlId{10066}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{10068}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{10072}{\htmlClass{Generalizable}{\text{e}}}}\, \,\href{Class.HasAdd.Core.html#162}{\htmlId{10074}{\htmlClass{Field Operator}{\text{+}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{10076}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{10079}{\htmlClass{Symbol}{\text{.}}}\,\,\href{Ledger.Dijkstra.Specification.PParams.html#4267}{\htmlId{10080}{\htmlClass{Field}{\text{drepActivity}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10093}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{10095}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6566}{\htmlId{10098}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6638}{\htmlId{10106}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{10115}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.Dec.html#2149}{\htmlId{10124}{\htmlClass{Function Operator}{\text{∪⁺}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10127}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{10129}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#6937}{\htmlId{10133}{\htmlClass{Generalizable}{\text{d}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10135}{\htmlClass{Field Operator}{\text{❵}}}}\, \end{pmatrix}$

  GOVCERT-deregdrep :
    ∙ c ∈ dom dReps
    ∙ (c , d) ∈ deposits
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{10254}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{10258}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7118}{\htmlId{10263}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6782}{\htmlId{10268}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7347}{\htmlId{10276}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6566}{\htmlId{10285}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6638}{\htmlId{10293}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{10302}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ deregdrep c d ,GOVCERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6566}{\htmlId{10342}{\htmlClass{Generalizable}{\text{dReps}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{10348}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10350}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{10352}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10354}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{10356}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6638}{\htmlId{10360}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{10369}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{10378}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10380}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{10382}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10384}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{10386}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \end{pmatrix}$

  GOVCERT-ccreghot :
    ∙ (c , nothing) ∉ ccKeys
    ∙ c ∈ cc
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{10501}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{10505}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7118}{\htmlId{10510}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6782}{\htmlId{10515}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7347}{\htmlId{10523}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6566}{\htmlId{10532}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6638}{\htmlId{10540}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{10549}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ ccreghot c mc ,GOVCERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6566}{\htmlId{10589}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Class.HasSingleton.html#288}{\htmlId{10597}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6985}{\htmlId{10599}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7012}{\htmlId{10603}{\htmlClass{Generalizable}{\text{mc}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10606}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{10608}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6638}{\htmlId{10611}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{10620}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$

-- CERT Transition System --
data _⊢_⇀⦇_,CERT⦈_  : CertEnv → CertState → DCert → CertState → Type where

  CERT-deleg :
    ∙ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{10760}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#2272}{\htmlId{10765}{\htmlClass{Field}{\text{PState.pools}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{10778}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Class.IsSet.html#916}{\htmlId{10784}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{10788}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Dijkstra.Specification.Certs.html#2436}{\htmlId{10789}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{10802}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{10805}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$ ⊢ stᵈ ⇀⦇ dCert ,DELEG⦈ stᵈ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{10884}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{10888}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7118}{\htmlId{10893}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6782}{\htmlId{10898}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7347}{\htmlId{10906}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7287}{\htmlId{10915}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{10921}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{10927}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7291}{\htmlId{10951}{\htmlClass{Generalizable}{\text{stᵈ'}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{10958}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{10964}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-pool :
    ∙ pp ⊢ stᵖ ⇀⦇ dCert ,POOL⦈ stᵖ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{11068}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{11072}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7118}{\htmlId{11077}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6782}{\htmlId{11082}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7347}{\htmlId{11090}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7287}{\htmlId{11099}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{11105}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{11111}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7287}{\htmlId{11135}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7331}{\htmlId{11141}{\htmlClass{Generalizable}{\text{stᵖ'}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{11148}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-gov :
    ∙ Γ ⊢ stᵍ ⇀⦇ dCert ,GOVCERT⦈ stᵍ'
      ────────────────────────────────
      Γ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7287}{\htmlId{11257}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{11263}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{11269}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7287}{\htmlId{11293}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{11299}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7311}{\htmlId{11305}{\htmlClass{Generalizable}{\text{stᵍ'}}}}\, \end{pmatrix}$


-- PRE-CERT Transition Rule --

open GovVote using (voter)

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

  CERT-pre :
    let refresh         = mapPartial (isGovVoterDRep ∘ voter) (fromList vs)
        refreshedDReps  = mapValueRestricted (const (e + pp .drepActivity)) dReps refresh
        wdrlCreds       = mapˢ stake (dom wdrls)
    in
    ∙ filter isKeyHash wdrlCreds ⊆ dom voteDelegs
    ∙ mapˢ (map₁ stake) (wdrls ˢ) ⊆ rewards ˢ
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{11827}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{11831}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7118}{\htmlId{11836}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6782}{\htmlId{11841}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7347}{\htmlId{11849}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6683}{\htmlId{11860}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6607}{\htmlId{11873}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6536}{\htmlId{11887}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{11897}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{11910}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6566}{\htmlId{11918}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6645}{\htmlId{11926}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6862}{\htmlId{11938}{\htmlClass{Generalizable}{\text{deposits'}}}}\, \end{pmatrix} \end{pmatrix}$ ⇀⦇ _ ,PRE-CERT⦈ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6683}{\htmlId{11972}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6607}{\htmlId{11985}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#11988}{\htmlId{11999}{\htmlClass{Function}{\text{constMap}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#11636}{\htmlId{12008}{\htmlClass{Bound}{\text{wdrlCreds}}}}\, \,\htmlId{12018}{\htmlClass{Number}{\text{0}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{12020}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6536}{\htmlId{12023}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{12033}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{12046}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#11546}{\htmlId{12054}{\htmlClass{Bound}{\text{refreshedDReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6645}{\htmlId{12071}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6862}{\htmlId{12083}{\htmlClass{Generalizable}{\text{deposits'}}}}\, \end{pmatrix} \end{pmatrix}$


-- POST-CERT Transition Rule --

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

  CERT-post :
    let activeVDelegs = mapˢ vDelegCredential (dom (DRepsOf stᵍ))
                         ∪ fromList (vDelegNoConfidence ∷ vDelegAbstain ∷ [])
    in
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7096}{\htmlId{12381}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{12385}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7118}{\htmlId{12390}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6782}{\htmlId{12395}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7347}{\htmlId{12403}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6683}{\htmlId{12414}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6607}{\htmlId{12427}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6536}{\htmlId{12441}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{12451}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{12464}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{12470}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ _ ,POST-CERT⦈ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6683}{\htmlId{12497}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \,\href{Axiom.Set.Map.html#17775}{\htmlId{12508}{\htmlClass{Function Operator}{\text{∣\^{}}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#12230}{\htmlId{12511}{\htmlClass{Bound}{\text{activeVDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6607}{\htmlId{12527}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6536}{\htmlId{12541}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6853}{\htmlId{12551}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7327}{\htmlId{12564}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7307}{\htmlId{12570}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$


-- CERTS Transition System --

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