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PDF cleanup: rename union symbol #254

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18 changes: 9 additions & 9 deletions src/Axiom/Set/Map.agda
Original file line number Diff line number Diff line change
Expand Up @@ -153,22 +153,22 @@ singletonᵐ a b = ❴ (a , b) ❵
❴ k , v ❵ᵐ = singletonᵐ k v

module Unionᵐ (sp-∈ : spec-∈ A) where
infixr 6 _∪ᵐˡ_
infixr 6 _∪ˡ_

_∪ᵐˡ'_ : Rel A B → Rel A B → Rel A B
m ∪ᵐˡ' m' = m ∪ filter (sp-∘ (sp-¬ (sp-∈ {dom m})) proj₁) m'
_∪ˡ'_ : Rel A B → Rel A B → Rel A B
m ∪ˡ' m' = m ∪ filter (sp-∘ (sp-¬ (sp-∈ {dom m})) proj₁) m'

_∪ᵐˡ_ : Map A B → Map A B → Map A B
m ∪ᵐˡ m' = disj-∪ m (filterᵐ (sp-∘ (sp-¬ sp-∈) proj₁) m')
_∪ˡ_ : Map A B → Map A B → Map A B
m ∪ˡ m' = disj-∪ m (filterᵐ (sp-∘ (sp-¬ sp-∈) proj₁) m')
(∈⇔P -⟨ (λ where x (_ , refl , hy) → proj₁ (∈⇔P hy) (∈⇔P x)) ⟩- ∈⇔P)

disjoint-∪ᵐˡ-∪ : (H : disjoint (dom R) (dom R')) → R ∪ᵐˡ' R' ≡ᵉ R ∪ R'
disjoint-∪ᵐˡ-∪ disj = from ≡ᵉ⇔≡ᵉ' λ _ → mk⇔
disjoint-∪ˡ-∪ : (H : disjoint (dom R) (dom R')) → R ∪ˡ' R' ≡ᵉ R ∪ R'
disjoint-∪ˡ-∪ disj = from ≡ᵉ⇔≡ᵉ' λ _ → mk⇔
(∈-∪⁺ ∘′ map₂ (proj₂ ∘′ ∈⇔P) ∘′ ∈⇔P)
(∈⇔P ∘′ map₂ (to ∈-filter ∘′ (λ h → (flip disj (∈-map⁺'' h)) , h)) ∘ ∈⇔P)

insert : Map A B → A → B → Map A B
insert m a b = ❴ a , b ❵ᵐ ∪ᵐˡ m
insert m a b = ❴ a , b ❵ᵐ ∪ˡ m

insertIfJust : ⦃ DecEq A ⦄ → A → Maybe B → Map A B → Map A B
insertIfJust x nothing m = m
Expand Down Expand Up @@ -281,7 +281,7 @@ module Restrictionᵐ (sp-∈ : spec-∈ A) where

-- map only values in X
mapValueRestricted : (B → B) → Map A B → Set A → Map A B
mapValueRestricted f m X = mapValues f (m ∣ X) ∪ᵐˡ m
mapValueRestricted f m X = mapValues f (m ∣ X) ∪ˡ m

-- map only value at a
mapSingleValue : (B → B) → Map A B → A → Map A B
Expand Down
26 changes: 13 additions & 13 deletions src/Axiom/Set/Sum.agda
Original file line number Diff line number Diff line change
Expand Up @@ -125,20 +125,20 @@ module _ ⦃ _ : DecEq A ⦄ ⦃ _ : DecEq B ⦄ where

open Unionᵐ sp-∈

ᵐˡ-finite : {R R' : Rel A B} → finite R → finite R' → finite (R ∪ᵐˡ' R')
ᵐˡ-finite Rᶠ R'ᶠ = ∪-preserves-finite Rᶠ
ˡ-finite : {R R' : Rel A B} → finite R → finite R' → finite (R ∪ˡ' R')
ˡ-finite Rᶠ R'ᶠ = ∪-preserves-finite Rᶠ
$ filter-finite (sp-∘ (sp-¬ sp-∈) _) (¬? ∘ ∈-A-dec ∘ _) R'ᶠ

_∪ᵐˡᶠ_ : FinMap A B → FinMap A B → FinMap A B
(_ , hX , Xᶠ) ∪ᵐˡᶠ (_ , hY , Yᶠ) =
toFinMap ((_ , hX) ∪ᵐˡ (_ , hY)) (∪ᵐˡ-finite Xᶠ Yᶠ)
_∪ˡᶠ_ : FinMap A B → FinMap A B → FinMap A B
(_ , hX , Xᶠ) ∪ˡᶠ (_ , hY , Yᶠ) =
toFinMap ((_ , hX) ∪ˡ (_ , hY)) (∪ˡ-finite Xᶠ Yᶠ)

indexedSumᵐ-∪ : ∀ {X Y : FinMap A B} {f}
→ disjoint (dom (toRel X)) (dom (toRel Y))
→ indexedSumᵐ f (X ∪ᵐˡᶠ Y) ≈ indexedSumᵐ f X ∙ indexedSumᵐ f Y
→ indexedSumᵐ f (X ∪ˡᶠ Y) ≈ indexedSumᵐ f X ∙ indexedSumᵐ f Y
indexedSumᵐ-∪ {X = X'@(X , _ , Xᶠ)} {Y'@(Y , _ , Yᶠ)} {f} disj = begin
indexedSumᵐ f (X' ∪ᵐˡᶠ Y') ≈⟨ indexedSum-cong {x = -, ∪ᵐˡ-finite Xᶠ Yᶠ} {(X ∪ Y) ᶠ}
$ disjoint-∪ᵐˡ-∪ disj ⟩
indexedSumᵐ f (X' ∪ˡᶠ Y') ≈⟨ indexedSum-cong {x = -, ∪ˡ-finite Xᶠ Yᶠ} {(X ∪ Y) ᶠ}
$ disjoint-∪ˡ-∪ disj ⟩
indexedSum f ((X ∪ Y) ᶠ) ≈⟨ indexedSum-∪ (disjoint-dom⇒disjoint disj) ⟩
indexedSumᵐ f X' ∙ indexedSumᵐ f Y' ∎
where instance _ = Xᶠ
Expand All @@ -147,14 +147,14 @@ module _ ⦃ _ : DecEq A ⦄ ⦃ _ : DecEq B ⦄ where
indexedSumᵐ-partition : ∀ {m m₁ m₂ : FinMap A B} {f} → toRel m ≡ toRel m₁ ⨿ toRel m₂
→ indexedSumᵐ f m ≈ indexedSumᵐ f m₁ ∙ indexedSumᵐ f m₂
indexedSumᵐ-partition {m} {m₁} {m₂} {f} m≡m₁∪m₂ = begin
indexedSumᵐ f m ≈⟨ indexedSumᵐ-cong {x = m} {m₁ ∪ᵐˡᶠ m₂} helper ⟩
indexedSumᵐ f (m₁ ∪ᵐˡᶠ m₂) ≈⟨ indexedSumᵐ-∪ {X = m₁} {Y = m₂} disj-dom' ⟩
indexedSumᵐ f m₁ ∙ indexedSumᵐ f m₂ ∎
indexedSumᵐ f m ≈⟨ indexedSumᵐ-cong {x = m} {m₁ ∪ˡᶠ m₂} helper ⟩
indexedSumᵐ f (m₁ ∪ˡᶠ m₂) ≈⟨ indexedSumᵐ-∪ {X = m₁} {Y = m₂} disj-dom' ⟩
indexedSumᵐ f m₁ ∙ indexedSumᵐ f m₂
where module ≡ᵉ = IsEquivalence ≡ᵉ-isEquivalence
disj-dom' = disj-dom {m = toMap m} {toMap m₁} {toMap m₂} m≡m₁∪m₂

helper : toRel m ≡ᵉ toRel (m₁ ∪ᵐˡᶠ m₂)
helper = ≡ᵉ.trans (proj₁ m≡m₁∪m₂) (≡ᵉ.sym $ disjoint-∪ᵐˡ-∪ disj-dom')
helper : toRel m ≡ᵉ toRel (m₁ ∪ˡᶠ m₂)
helper = ≡ᵉ.trans (proj₁ m≡m₁∪m₂) (≡ᵉ.sym $ disjoint-∪ˡ-∪ disj-dom')

syntax indexedSumᵐ (λ a → x) m = Σᵐ[ a ← m ] x
syntax indexedSumᵐᵛ (λ a → x) m = Σᵐᵛ[ a ← m ] x
8 changes: 4 additions & 4 deletions src/Ledger/Deleg.lagda
Original file line number Diff line number Diff line change
Expand Up @@ -123,18 +123,18 @@ data _⊢_⇀⦇_,POOL⦈_ : PoolEnv → PState → DCert → PState → Set whe
c ∉ dom pools
────────────────────────────────
pp ⊢ ⟦ pools , retiring ⟧ᵖ ⇀⦇ regpool c poolParams ,POOL⦈
⟦ ❴ c , poolParams ❵ᵐ ∪ᵐˡ pools , retiring ⟧ᵖ
⟦ ❴ c , poolParams ❵ᵐ ∪ˡ pools , retiring ⟧ᵖ

POOL-retirepool :
pp ⊢ ⟦ pools , retiring ⟧ᵖ ⇀⦇ retirepool c e ,POOL⦈
⟦ pools , ❴ c , e ❵ᵐ ∪ᵐˡ retiring ⟧ᵖ
⟦ pools , ❴ c , e ❵ᵐ ∪ˡ retiring ⟧ᵖ

data _⊢_⇀⦇_,GOVCERT⦈_ : GovCertEnv → GState → DCert → GState → Set where
GOVCERT-regdrep : let open PParams pp in
(d ≡ drepDeposit × c ∉ dom dReps) ⊎ (d ≡ 0 × c ∈ dom dReps)
────────────────────────────────
⟦ e , pp , vs ⟧ᶜ ⊢ ⟦ dReps , ccKeys ⟧ᵛ ⇀⦇ regdrep c d an ,GOVCERT⦈
⟦ ❴ c , e + drepActivity ❵ᵐ ∪ᵐˡ dReps , ccKeys ⟧ᵛ
⟦ ❴ c , e + drepActivity ❵ᵐ ∪ˡ dReps , ccKeys ⟧ᵛ

GOVCERT-deregdrep :
c ∈ dom dReps
Expand All @@ -146,7 +146,7 @@ data _⊢_⇀⦇_,GOVCERT⦈_ : GovCertEnv → GState → DCert → GState → S
(c , nothing) ∉ ccKeys
────────────────────────────────
Γ ⊢ ⟦ dReps , ccKeys ⟧ᵛ ⇀⦇ ccreghot c mc ,GOVCERT⦈
⟦ dReps , singletonᵐ c mc ∪ᵐˡ ccKeys ⟧ᵛ
⟦ dReps , singletonᵐ c mc ∪ˡ ccKeys ⟧ᵛ
\end{code}
\caption{Auxiliary DELEG and POOL rules}
\end{figure*}
Expand Down
2 changes: 1 addition & 1 deletion src/Ledger/GovernanceActions.lagda
Original file line number Diff line number Diff line change
Expand Up @@ -322,7 +322,7 @@ data _⊢_⇀⦇_,ENACT⦈_ : EnactEnv → EnactState → GovAction → EnactSta
∀[ term ∈ range new ] term ≤ (s .pparams .proj₁ .PParams.ccMaxTermLength +ᵉ e)
────────────────────────────────
⟦ gid , t , e ⟧ᵉ ⊢ s ⇀⦇ NewCommittee new rem q ,ENACT⦈
record s { cc = just ((new ∪ᵐˡ old) ∣ rem ᶜ , q) , gid }
record s { cc = just ((new ∪ˡ old) ∣ rem ᶜ , q) , gid }

Enact-NewConst :
⟦ gid , t , e ⟧ᵉ ⊢ s ⇀⦇ NewConstitution dh sh ,ENACT⦈
Expand Down
4 changes: 2 additions & 2 deletions src/Ledger/PPUp.lagda
Original file line number Diff line number Diff line change
Expand Up @@ -95,7 +95,7 @@ data _⊢_⇀⦇_,PPUP⦈_ : PPUpdateEnv → PPUpdateState → Maybe Update →
→ epoch slot ≡ e
────────────────────────────────
Γ ⊢ record { pup = pupˢ ; fpup = fpupˢ } ⇀⦇ just (pup , e) ,PPUP⦈
record { pup = pup ∪ᵐˡ pupˢ ; fpup = fpupˢ }
record { pup = pup ∪ˡ pupˢ ; fpup = fpupˢ }

PPUpdateFuture : let open PPUpdateEnv Γ in
dom pup ⊆ dom genDelegs
Expand All @@ -104,7 +104,7 @@ data _⊢_⇀⦇_,PPUP⦈_ : PPUpdateEnv → PPUpdateState → Maybe Update →
→ sucᵉ (epoch slot) ≡ e
────────────────────────────────
Γ ⊢ record { pup = pupˢ ; fpup = fpupˢ } ⇀⦇ just (pup , e) ,PPUP⦈
record { pup = pupˢ ; fpup = pup ∪ᵐˡ fpupˢ }
record { pup = pupˢ ; fpup = pup ∪ˡ fpupˢ }
\end{code}
\caption{PPUP inference rules}
\end{figure*}
22 changes: 11 additions & 11 deletions src/Ledger/Ratify.lagda
Original file line number Diff line number Diff line change
Expand Up @@ -229,17 +229,17 @@ restrictedDists coins rank dists = dists
where open StakeDistrs dists
-- one always includes the other
restrict : Credential ⇀ Coin → Credential ⇀ Coin
restrict dist = topNDRepDist rank dist ∪ᵐˡ mostStakeDRepDist dist coins
restrict dist = topNDRepDist rank dist ∪ˡ mostStakeDRepDist dist coins
\end{code}
\begin{figure*}[h!]
{\small
\begin{code}
actualVotes : RatifyEnv → CCData → (GovRole × Credential) ⇀ Vote → GovAction → PParams
→ VDeleg ⇀ Vote
actualVotes Γ cc votes ga pparams
= mapKeys (credVoter CC) actualCCVotes
ᵐˡ actualPDRepVotes ∪ᵐˡ actualDRepVotes
ᵐˡ actualSPOVotes
= mapKeys (credVoter CC) actualCCVotes
ˡ actualPDRepVotes ∪ˡ actualDRepVotes
ˡ actualSPOVotes
where
open RatifyEnv Γ
open PParams pparams
Expand Down Expand Up @@ -267,17 +267,17 @@ actualVotes Γ cc votes ga pparams
(nothing , _) → ∅ᵐ

actualPDRepVotes
= ❴ abstainRep , Vote.abstain ❵ᵐ
ᵐˡ ❴ noConfidenceRep , (case ga of λ where NoConfidence → Vote.yes
_ → Vote.no) ❵ᵐ
= ❴ abstainRep , Vote.abstain ❵ᵐ
ˡ ❴ noConfidenceRep , (case ga of λ where NoConfidence → Vote.yes
_ → Vote.no) ❵ᵐ

actualDRepVotes
= roleVotes GovRole.DRep
ᵐˡ constMap (mapˢ (credVoter DRep) activeDReps) Vote.no
= roleVotes GovRole.DRep
ˡ constMap (mapˢ (credVoter DRep) activeDReps) Vote.no

actualSPOVotes
= roleVotes GovRole.SPO
ᵐˡ constMap spos (if isHF then Vote.no else Vote.abstain)
= roleVotes GovRole.SPO
ˡ constMap spos (if isHF then Vote.no else Vote.abstain)
where
spos : ℙ VDeleg
spos = filterˢ isSPOProp $ dom (StakeDistrs.stakeDistr stakeDistrs)
Expand Down
2 changes: 1 addition & 1 deletion src/Ledger/Utxo.lagda
Original file line number Diff line number Diff line change
Expand Up @@ -319,7 +319,7 @@ data _⊢_⇀⦇_,UTXO⦈_ where
-- Add deposits

────────────────────────────────
Γ ⊢ s ⇀⦇ tx ,UTXO⦈ ⟦ (utxo ∣ txins ᶜ) ∪ᵐˡ (outs txb)
Γ ⊢ s ⇀⦇ tx ,UTXO⦈ ⟦ (utxo ∣ txins ᶜ) ∪ˡ outs txb
, fees + txfee
, updateDeposits pp txb deposits
, donations + txdonation
Expand Down
42 changes: 21 additions & 21 deletions src/Ledger/Utxo/Properties.lagda
Original file line number Diff line number Diff line change
Expand Up @@ -60,13 +60,13 @@ private
∙-homo-Coin = IsMagmaHomomorphism.homo (isMagmaHomomorphism coinIsMonoidHomomorphism)

balance-∪ : disjoint (dom utxo) (dom utxo')
→ cbalance (utxo ∪ᵐˡ utxo') ≡ cbalance utxo + cbalance utxo'
→ cbalance (utxo ∪ˡ utxo') ≡ cbalance utxo + cbalance utxo'
balance-∪ {utxo} {utxo'} h = begin
cbalance (utxo ∪ᵐˡ utxo')
cbalance (utxo ∪ˡ utxo')
≡⟨ ⟦⟧-cong coinIsMonoidHomomorphism
$ indexedSumᵐ-cong {x = (utxo ∪ᵐˡ utxo') ᶠᵐ} {(utxo ᶠᵐ) ∪ᵐˡᶠ (utxo' ᶠᵐ)} (id , id)
$ indexedSumᵐ-cong {x = (utxo ∪ˡ utxo') ᶠᵐ} {(utxo ᶠᵐ) ∪ˡᶠ (utxo' ᶠᵐ)} (id , id)
coin (indexedSumᵐ _ ((utxo ᶠᵐ) ∪ᵐˡᶠ (utxo' ᶠᵐ)))
coin (indexedSumᵐ _ ((utxo ᶠᵐ) ∪ˡᶠ (utxo' ᶠᵐ)))
≡⟨ ⟦⟧-cong coinIsMonoidHomomorphism
$ indexedSumᵐ-∪ {X = utxo ᶠᵐ} {utxo' ᶠᵐ} h
Expand Down Expand Up @@ -249,15 +249,15 @@ module DepositHelpers

utxo-ref-prop :
cbalance utxo + ref ≡
(cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) + txfee) + txdonation + tot
(cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) + txfee) + txdonation + tot
utxo-ref-prop = begin
cbalance utxo + ref
≡˘⟨ cong (_+ ref)
$ balance-cong-coin {utxo = (utxo ∣ txins ᶜ) ∪ᵐˡ (utxo ∣ txins)}{utxo}
$ disjoint-∪ᵐˡ-∪ (disjoint-sym res-ex-disjoint)
$ balance-cong-coin {utxo = (utxo ∣ txins ᶜ) ∪ˡ (utxo ∣ txins)}{utxo}
$ disjoint-∪ˡ-∪ (disjoint-sym res-ex-disjoint)
≡ᵉ-∘ ∪-sym
≡ᵉ-∘ res-ex-∪ (_∈? txins) ⟩
cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ (utxo ∣ txins)) + ref
cbalance ((utxo ∣ txins ᶜ) ∪ˡ (utxo ∣ txins)) + ref
≡⟨ cong (_+ ref)
$ balance-∪ {utxo ∣ txins ᶜ} {utxo ∣ txins}
$ flip res-ex-disjoint ⟩
Expand All @@ -273,17 +273,17 @@ module DepositHelpers
ℕ.+ tot ℕ.+ txdonation
≡˘⟨ cong (λ x → (x + txfee) + tot + txdonation)
$ balance-∪ {utxo ∣ txins ᶜ} {outs txb} h ⟩
(cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) ℕ.+ txfee)
(cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) ℕ.+ txfee)
ℕ.+ tot ℕ.+ txdonation
≡t⟨⟩
(cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) ℕ.+ txfee)
(cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) ℕ.+ txfee)
ℕ.+ (tot ℕ.+ txdonation)
≡⟨ cong ((cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) + txfee) +_)
≡⟨ cong ((cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) + txfee) +_)
$ +-comm tot txdonation ⟩
(cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) ℕ.+ txfee)
(cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) ℕ.+ txfee)
ℕ.+ (txdonation ℕ.+ tot)
≡t⟨⟩
(cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) ℕ.+ txfee)
(cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) ℕ.+ txfee)
ℕ.+ txdonation ℕ.+ tot
∎ where open IsEquivalence ≡ᵉ-isEquivalence renaming (trans to infixl 4 _≡ᵉ-∘_)

Expand Down Expand Up @@ -380,24 +380,24 @@ pov {tx}{utxo}{_}{fees}{deposits}{donations}
≡t⟨⟩
cbalance utxo ℕ.+ ref ℕ.+ (remDepTot ℕ.+ fees)
≡⟨ cong (_+ (remDepTot + fees)) utxo-ref-prop ⟩
(cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) ℕ.+ txfee)
(cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) ℕ.+ txfee)
ℕ.+ txdonation ℕ.+ tot ℕ.+ (remDepTot ℕ.+ fees)
≡t⟨⟩
cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb)
cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb)
ℕ.+ (txfee ℕ.+ txdonation ℕ.+ (tot ℕ.+ remDepTot) ℕ.+ fees)
≡⟨ cong (cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb) +_) rearrange0 ⟩
cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb)
≡⟨ cong (cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb) +_) rearrange0 ⟩
cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb)
+ ((fees + txfee) + getCoin deposits' + txdonation)
∎ ⟩
cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb)
cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb)
ℕ.+ ((fees + txfee) ℕ.+ getCoin deposits' ℕ.+ txdonation) ℕ.+ donations
≡t⟨⟩
cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb)
cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb)
ℕ.+ (fees + txfee) ℕ.+ getCoin deposits' ℕ.+ (txdonation ℕ.+ donations)
≡⟨ cong (cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb)
≡⟨ cong (cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb)
+ (fees + txfee) + getCoin deposits' ℕ.+_)
$ +-comm txdonation donations ⟩
cbalance ((utxo ∣ txins ᶜ) ∪ᵐˡ outs txb)
cbalance ((utxo ∣ txins ᶜ) ∪ˡ outs txb)
+ (fees + txfee) + getCoin deposits' + (donations + txdonation)
\end{code}
Expand Down
2 changes: 1 addition & 1 deletion src/latex/agda-latex-macros.sty
Original file line number Diff line number Diff line change
Expand Up @@ -177,7 +177,7 @@
\newcommand{\Credential}{\AgdaFunction{Credential}\xspace}
\newcommand{\credVoter}{\AgdaInductiveConstructor{credVoter}\xspace}
\newcommand{\Crypto}{\AgdaRecord{Crypto}\xspace}
\newcommand{\cupsupermsuperl}{\AgdaFunction{∪ᵐˡ}\xspace}
\newcommand{\cupsupermsuperl}{\AgdaFunction{∪ˡ}\xspace}
\newcommand{\cupsuperplus}{\AgdaFunction{∪⁺}\xspace}
\newcommand{\currentEpoch}{\AgdaField{currentEpoch}\xspace}

Expand Down