{-# 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 import Ledger.Dijkstra.Specification.Account gs
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

applyDirectDeposits : DirectDeposits → DState → DState
applyDirectDeposits dd ds = record ds { rewards = RewardsOf ds ∪⁺ dd }


applyWithdrawals : Withdrawals → Rewards → Rewards
applyWithdrawals wdrls rwds =
  foldl applyOne rwds (setToList (wdrls ˢ))
  where
    -- For each withdrawal entry `(addr, amt)`, look up `stake addr` in the acc,
    -- compute `bal ∸ amt`, create a singleton map with the new balance, and
    -- merge it with the rest (complement-restricted, to remove the old entry).
    applyOne : Rewards → RewardAddress × Coin → Rewards
    applyOne acc (addr , amt) =
      case lookupᵐ? acc (stake addr) of λ where
        (just bal) → ❴ stake addr , bal ∸ amt ❵ ∪ˡ (acc ∣ ❴ stake addr ❵ ᶜ)
        nothing    → acc
        -- `nothing` case is defensive; the PRE-CERT precondition guarantees the
        -- credential is registered, but handling it makes the function total.


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 ≡ 0)
    ∙ mvd ∈ mapˢ (just ∘ vDelegCredential) delegatees ∪
            fromList ( nothing ∷ just vDelegAbstain ∷ just vDelegNoConfidence ∷ [] )
    ∙ mkh ∈ mapˢ just (dom pools) ∪ ❴ nothing ❵
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{8772}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{8777}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6931}{\htmlId{8785}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6561}{\htmlId{8802}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6485}{\htmlId{8812}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6417}{\htmlId{8822}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{8829}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ delegate c mvd mkh d ,DELEG⦈ $\begin{pmatrix} \,\href{Axiom.Set.Map.html#9262}{\htmlId{8874}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{8887}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7143}{\htmlId{8889}{\htmlClass{Generalizable}{\text{mvd}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6561}{\htmlId{8893}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Axiom.Set.Map.html#9262}{\htmlId{8903}{\htmlClass{Function}{\text{insertIfJust}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{8916}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7057}{\htmlId{8918}{\htmlClass{Generalizable}{\text{mkh}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6485}{\htmlId{8922}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6417}{\htmlId{8932}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{8937}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8940}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{8942}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\htmlId{8946}{\htmlClass{Number}{\text{0}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8948}{\htmlClass{Field Operator}{\text{❵}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{8952}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.Dec.html#2149}{\htmlId{8961}{\htmlClass{Function Operator}{\text{∪⁺}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8964}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{8966}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#6823}{\htmlId{8970}{\htmlClass{Generalizable}{\text{d}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{8972}{\htmlClass{Field Operator}{\text{❵}}}}\, \end{pmatrix}$

  DELEG-dereg :
    ∙ (c , 0) ∈ rwds
    ∙ (c , d) ∈ deposits
    ∙ md ≡ nothing ⊎ md ≡ just d
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{9119}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{9124}{\htmlClass{Generalizable}{\text{pools}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6931}{\htmlId{9132}{\htmlClass{Generalizable}{\text{delegatees}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6561}{\htmlId{9149}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6485}{\htmlId{9159}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6417}{\htmlId{9169}{\htmlClass{Generalizable}{\text{rwds}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{9176}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ dereg c md ,DELEG⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6561}{\htmlId{9211}{\htmlClass{Generalizable}{\text{vDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9219}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9221}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{9223}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9225}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9227}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6485}{\htmlId{9231}{\htmlClass{Generalizable}{\text{sDelegs}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9239}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9241}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{9243}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9245}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9247}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6417}{\htmlId{9251}{\htmlClass{Generalizable}{\text{rwds}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9256}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9258}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{9260}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9262}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9264}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{9268}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9277}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9279}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{9281}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9283}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{9285}{\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 ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{9607}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6605}{\htmlId{9624}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6632}{\htmlId{9642}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{9662}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$ ⇀⦇ regpool kh poolParams ,POOL⦈ $\begin{pmatrix}
           \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{9727}{\htmlClass{Generalizable}{\text{pools}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{9733}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9736}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7033}{\htmlId{9738}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7087}{\htmlId{9743}{\htmlClass{Generalizable}{\text{poolParams}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9754}{\htmlClass{Field Operator}{\text{❵}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6605}{\htmlId{9767}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6632}{\htmlId{9785}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{9805}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{9814}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9817}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7033}{\htmlId{9819}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{9824}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{9827}{\htmlClass{Symbol}{\text{.}}}\,\,\href{Ledger.Dijkstra.Specification.PParams.html#2416}{\htmlId{9828}{\htmlClass{Field}{\text{poolDeposit}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{9840}{\htmlClass{Field Operator}{\text{❵}}}}\,
         \end{pmatrix}$

  POOL-rereg :
    ∙ Is-just (isPoolRegistered pools kh)
    ────────────────────────────────
    pp ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{9959}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6605}{\htmlId{9976}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6632}{\htmlId{9994}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{10014}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$ ⇀⦇ regpool kh poolParams ,POOL⦈ $\begin{pmatrix}
           \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{10079}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Class.HasSingleton.html#288}{\htmlId{10096}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7033}{\htmlId{10098}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#7087}{\htmlId{10103}{\htmlClass{Generalizable}{\text{poolParams}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10114}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{10116}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6605}{\htmlId{10119}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6632}{\htmlId{10137}{\htmlClass{Generalizable}{\text{retiring}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{10146}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10148}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7033}{\htmlId{10150}{\htmlClass{Generalizable}{\text{kh}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10153}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{10155}{\htmlClass{Function Operator}{\text{ᶜ}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{10168}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$

  POOL-retirepool :
    ────────────────────────────────
    pp ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{10257}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6605}{\htmlId{10274}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6632}{\htmlId{10292}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{10312}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$ ⇀⦇ retirepool kh e ,POOL⦈ $\begin{pmatrix}
           \,\href{Ledger.Dijkstra.Specification.Certs.html#6599}{\htmlId{10371}{\htmlClass{Generalizable}{\text{pools}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6605}{\htmlId{10388}{\htmlClass{Generalizable}{\text{fPools}}}}\,
         \\ \,\href{Class.HasSingleton.html#288}{\htmlId{10406}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7033}{\htmlId{10408}{\htmlClass{Generalizable}{\text{kh}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{10413}{\htmlClass{Generalizable}{\text{e}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10415}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{10417}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6632}{\htmlId{10420}{\htmlClass{Generalizable}{\text{retiring}}}}\,
         \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{10440}{\htmlClass{Generalizable}{\text{deposits}}}}\,
         \end{pmatrix}$


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

  GOVCERT-regdrep :
    ∙ (d ≡ pp .drepDeposit × c ∉ dom dReps) ⊎ (d ≡ 0 × c ∈ dom dReps)
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{10713}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{10717}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7004}{\htmlId{10722}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{10727}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{10735}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6452}{\htmlId{10744}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6524}{\htmlId{10752}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{10761}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ regdrep c d an ,GOVCERT⦈ $\begin{pmatrix} \,\href{Class.HasSingleton.html#288}{\htmlId{10802}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{10804}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{10808}{\htmlClass{Generalizable}{\text{e}}}}\, \,\href{Class.HasAdd.Core.html#162}{\htmlId{10810}{\htmlClass{Field Operator}{\text{+}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{10812}{\htmlClass{Generalizable}{\text{pp}}}}\, \,\htmlId{10815}{\htmlClass{Symbol}{\text{.}}}\,\,\href{Ledger.Dijkstra.Specification.PParams.html#3546}{\htmlId{10816}{\htmlClass{Field}{\text{drepActivity}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10829}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{10831}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6452}{\htmlId{10834}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6524}{\htmlId{10842}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{10851}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.Dec.html#2149}{\htmlId{10860}{\htmlClass{Function Operator}{\text{∪⁺}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10863}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{10865}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#6823}{\htmlId{10869}{\htmlClass{Generalizable}{\text{d}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{10871}{\htmlClass{Field Operator}{\text{❵}}}}\, \end{pmatrix}$

  GOVCERT-deregdrep :
    ∙ c ∈ dom dReps
    ∙ (c , d) ∈ deposits
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{10990}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{10994}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7004}{\htmlId{10999}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{11004}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{11012}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6452}{\htmlId{11021}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6524}{\htmlId{11029}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{11038}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ deregdrep c d ,GOVCERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6452}{\htmlId{11078}{\htmlClass{Generalizable}{\text{dReps}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{11084}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{11086}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{11088}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{11090}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{11092}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6524}{\htmlId{11096}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{11105}{\htmlClass{Generalizable}{\text{deposits}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{11114}{\htmlClass{Function Operator}{\text{∣}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{11116}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{11118}{\htmlClass{Generalizable}{\text{c}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{11120}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#13606}{\htmlId{11122}{\htmlClass{Function Operator}{\text{ᶜ}}}}\, \end{pmatrix}$

  GOVCERT-ccreghot :
    ∙ (c , nothing) ∉ ccKeys
    ∙ c ∈ cc
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{11237}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{11241}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7004}{\htmlId{11246}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{11251}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{11259}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6452}{\htmlId{11268}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6524}{\htmlId{11276}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{11285}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$ ⇀⦇ ccreghot c mc ,GOVCERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6452}{\htmlId{11325}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Class.HasSingleton.html#288}{\htmlId{11333}{\htmlClass{Field Operator}{\text{❴}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6871}{\htmlId{11335}{\htmlClass{Generalizable}{\text{c}}}}\, , \,\href{Ledger.Dijkstra.Specification.Certs.html#6898}{\htmlId{11339}{\htmlClass{Generalizable}{\text{mc}}}}\, \,\href{Class.HasSingleton.html#288}{\htmlId{11342}{\htmlClass{Field Operator}{\text{❵}}}}\, \,\href{Axiom.Set.Map.html#7640}{\htmlId{11344}{\htmlClass{Function Operator}{\text{∪ˡ}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6524}{\htmlId{11347}{\htmlClass{Generalizable}{\text{ccKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{11356}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix}$

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

  CERT-deleg :
    ∙ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{11496}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#2172}{\htmlId{11501}{\htmlClass{Field}{\text{PState.pools}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{11514}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Class.IsSet.html#916}{\htmlId{11520}{\htmlClass{Function}{\text{dom}}}}\, \,\htmlId{11524}{\htmlClass{Symbol}{\text{(}}}\,\,\href{Ledger.Dijkstra.Specification.Certs.html#2338}{\htmlId{11525}{\htmlClass{Field}{\text{GState.dreps}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{11538}{\htmlClass{Generalizable}{\text{stᵍ}}}}\,\,\htmlId{11541}{\htmlClass{Symbol}{\text{)}}}\, \end{pmatrix}$ ⊢ stᵈ ⇀⦇ dCert ,DELEG⦈ stᵈ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{11620}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{11624}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7004}{\htmlId{11629}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{11634}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{11642}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7173}{\htmlId{11651}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{11657}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{11663}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7177}{\htmlId{11687}{\htmlClass{Generalizable}{\text{stᵈ'}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{11694}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{11700}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-pool :
    ∙ pp ⊢ stᵖ ⇀⦇ dCert ,POOL⦈ stᵖ'
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{11804}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{11808}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7004}{\htmlId{11813}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{11818}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{11826}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7173}{\htmlId{11835}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{11841}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{11847}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7173}{\htmlId{11871}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7217}{\htmlId{11877}{\htmlClass{Generalizable}{\text{stᵖ'}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{11884}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$

  CERT-gov :
    ∙ Γ ⊢ stᵍ ⇀⦇ dCert ,GOVCERT⦈ stᵍ'
      ────────────────────────────────
      Γ ⊢ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7173}{\htmlId{11993}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{11999}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{12005}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ dCert ,CERT⦈ $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#7173}{\htmlId{12029}{\htmlClass{Generalizable}{\text{stᵈ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{12035}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7197}{\htmlId{12041}{\htmlClass{Generalizable}{\text{stᵍ'}}}}\, \end{pmatrix}$


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
    ∙ wdrlCreds ⊆ dom rewards
    ∙ ∀[ (addr , amt) ∈ wdrls ˢ ] amt ≤ maybe id 0 (lookupᵐ? rewards (stake addr))
      ────────────────────────────────
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{12599}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{12603}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7004}{\htmlId{12608}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{12613}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{12621}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6569}{\htmlId{12632}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6493}{\htmlId{12645}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6422}{\htmlId{12659}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{12669}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{12682}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6452}{\htmlId{12690}{\htmlClass{Generalizable}{\text{dReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6531}{\htmlId{12698}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6748}{\htmlId{12710}{\htmlClass{Generalizable}{\text{deposits'}}}}\, \end{pmatrix} \end{pmatrix}$ ⇀⦇ _ ,PRE-CERT⦈ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6569}{\htmlId{12744}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6493}{\htmlId{12757}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7457}{\htmlId{12771}{\htmlClass{Function}{\text{applyWithdrawals}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{12788}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#6422}{\htmlId{12794}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{12804}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{12817}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#12251}{\htmlId{12825}{\htmlClass{Bound}{\text{refreshedDReps}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6531}{\htmlId{12842}{\htmlClass{Generalizable}{\text{ccHotKeys}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6748}{\htmlId{12854}{\htmlClass{Generalizable}{\text{deposits'}}}}\, \end{pmatrix} \end{pmatrix}$


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

  CERT-post :
    let activeVDelegs = mapˢ vDelegCredential (dom (DRepsOf stᵍ))
                         ∪ fromList (vDelegNoConfidence ∷ vDelegAbstain ∷ [])
    in
      $\begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6982}{\htmlId{13119}{\htmlClass{Generalizable}{\text{e}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7119}{\htmlId{13123}{\htmlClass{Generalizable}{\text{pp}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7004}{\htmlId{13128}{\htmlClass{Generalizable}{\text{vs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6668}{\htmlId{13133}{\htmlClass{Generalizable}{\text{wdrls}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7233}{\htmlId{13141}{\htmlClass{Generalizable}{\text{cc}}}}\, \end{pmatrix}$ ⊢ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6569}{\htmlId{13152}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6493}{\htmlId{13165}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6422}{\htmlId{13179}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{13189}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{13202}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{13208}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$ ⇀⦇ _ ,POST-CERT⦈ $\begin{pmatrix} \begin{pmatrix} \,\href{Ledger.Dijkstra.Specification.Certs.html#6569}{\htmlId{13235}{\htmlClass{Generalizable}{\text{voteDelegs}}}}\, \,\href{Axiom.Set.Map.html#17775}{\htmlId{13246}{\htmlClass{Function Operator}{\text{∣\^{}}}}}\, \,\href{Ledger.Dijkstra.Specification.Certs.html#12968}{\htmlId{13249}{\htmlClass{Bound}{\text{activeVDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6493}{\htmlId{13265}{\htmlClass{Generalizable}{\text{stakeDelegs}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6422}{\htmlId{13279}{\htmlClass{Generalizable}{\text{rewards}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#6739}{\htmlId{13289}{\htmlClass{Generalizable}{\text{deposits}}}}\, \end{pmatrix} \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7213}{\htmlId{13302}{\htmlClass{Generalizable}{\text{stᵖ}}}}\, \\ \,\href{Ledger.Dijkstra.Specification.Certs.html#7193}{\htmlId{13308}{\htmlClass{Generalizable}{\text{stᵍ}}}}\, \end{pmatrix}$


-- CERTS Transition System --

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