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favonia committed Nov 21, 2023
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10 changes: 5 additions & 5 deletions src/Mugen/Algebra/Displacement.agda
Original file line number Diff line number Diff line change
Expand Up @@ -95,7 +95,7 @@ module _
Iso→is-hlevel 1 eqv $
Σ-is-hlevel 1 (Y.has-is-set _ _) λ _
Π-is-hlevel² 1 λ _ _ Y.has-is-set _ _
where unquoteDecl eqv = declare-record-iso eqv (quote is-displacement-algebra-hom)
where unquoteDecl eqv = declare-record-iso eqv (quote is-displacement-algebra-hom)

record Displacement-algebra-hom : Type (o ⊔ o' ⊔ r ⊔ r') where
no-eta-equality
Expand Down Expand Up @@ -152,7 +152,7 @@ displacement-hom-∘ f g .strict-hom =
strictly-monotone-∘ (f .strict-hom) (g .strict-hom)
displacement-hom-∘ f g .has-is-displacement-hom .is-displacement-algebra-hom.pres-ε =
ap (λ x f # x) (g .pres-ε)
∙ f .pres-ε
∙ f .pres-ε
displacement-hom-∘ f g .has-is-displacement-hom .is-displacement-algebra-hom.pres-⊗ x y =
ap (λ x f # x) (g .pres-⊗ x y)
∙ f .pres-⊗ (g # x) (g # y)
Expand Down Expand Up @@ -302,7 +302,7 @@ module _
identity : (a : ⌞ A ⌟) α a B.ε ≡ a
compat : (a : ⌞ A ⌟) (x y : ⌞ B ⌟) α (α a x) y ≡ α a (x B.⊗ y)
invariant : (a : ⌞ A ⌟) (x y : ⌞ B ⌟) x B.< y α a x A.< α a y

is-right-displacement-action-is-prop
:: ⌞ A ⌟ ⌞ B ⌟ ⌞ A ⌟)
is-prop (is-right-displacement-action α)
Expand All @@ -311,7 +311,7 @@ module _
Σ-is-hlevel 1 (Π-is-hlevel 1 λ _ A.has-is-set _ _) λ _
Σ-is-hlevel 1 (Π-is-hlevel³ 1 λ _ _ _ A.has-is-set _ _) λ _
Π-is-hlevel³ 1 λ _ _ _ Π-is-hlevel 1 λ _ A.<-thin
where unquoteDecl eqv = declare-record-iso eqv (quote is-right-displacement-action)
where unquoteDecl eqv = declare-record-iso eqv (quote is-right-displacement-action)

record Right-displacement-action
{o r o′ r′}
Expand All @@ -326,7 +326,7 @@ record Right-displacement-action

module _ where
open Right-displacement-action

Right-displacement-action-path
: {o r o′ r′}
{A : Strict-order o r} {B : Displacement-algebra o′ r′}
Expand Down
8 changes: 4 additions & 4 deletions src/Mugen/Algebra/Displacement/Coimage.agda
Original file line number Diff line number Diff line change
Expand Up @@ -54,10 +54,10 @@ module Coim-of-displacement-hom
-- Algebra

_⊗coim_ : X/f X/f X/f
_⊗coim_ = Coim-map₂ (λ x y x X.⊗ y) λ w x y z p q
(pres-⊗ w y ∙ ap₂ Y._⊗_ p q ∙ sym (pres-⊗ x z))
_⊗coim_ = Coim-map₂ (λ x y x X.⊗ y) λ w x y z p q
(pres-⊗ w y ∙ ap₂ Y._⊗_ p q ∙ sym (pres-⊗ x z))

εcoim : X/f
εcoim : X/f
εcoim = inc X.ε

⊗coim-idl : x εcoim ⊗coim x ≡ x
Expand Down Expand Up @@ -167,7 +167,7 @@ module _ {o r} {X Y : Displacement-algebra o r} {f : Displacement-algebra-hom X
(Y-joins.universal (coim≤→Y≤ x≤z) (coim≤→Y≤ y≤z))

joins : has-joins (Coim-of-displacement-hom f)
joins .has-joins.join = coim-join
joins .has-joins.join = coim-join
joins .has-joins.joinl {x} {y} =
Coim-elim-prop₂ {C = λ x y x coim≤ (coim-join x y)}
(λ x y X/f.≤-thin) coim-joinl x y
Expand Down
4 changes: 2 additions & 2 deletions src/Mugen/Algebra/Displacement/FiniteSupport.agda
Original file line number Diff line number Diff line change
Expand Up @@ -68,7 +68,7 @@ module FinSupport {o r} (𝒟 : Displacement-algebra o r) (cmp : ∀ x y → Tri
merge-fin : FinSupportList FinSupportList FinSupportList
merge-fin xs ys .FinSupportList.support = merge (xs .support) (ys .support)
merge-fin xs ys .FinSupportList.is-ε = ap₂ _⊗_ (xs .is-ε) (ys .is-ε) ∙ 𝒟.idl

empty-fin : FinSupportList
empty-fin .support = empty
empty-fin .is-ε = refl
Expand Down Expand Up @@ -126,7 +126,7 @@ module _
where
open FinSupport 𝒟 cmp
open FinSupportList

FinSupport⊆NearlyConstant : is-displacement-subalgebra (FiniteSupport 𝒟 cmp) (NearlyConstant 𝒟 cmp)
FinSupport⊆NearlyConstant = to-displacement-subalgebra mk where
mk : make-displacement-subalgebra _ _
Expand Down
10 changes: 5 additions & 5 deletions src/Mugen/Algebra/Displacement/InfiniteProduct.agda
Original file line number Diff line number Diff line change
Expand Up @@ -31,13 +31,13 @@ module Inf {o r} (𝒟 : Displacement-algebra o r) where
ε∞ _ = ε

⊗∞-associative : (f g h : Nat ⌞ 𝒟 ⌟) (f ⊗∞ (g ⊗∞ h)) ≡ ((f ⊗∞ g) ⊗∞ h)
⊗∞-associative f g h = funext λ x 𝒟.associative
⊗∞-associative f g h = funext λ x 𝒟.associative

⊗∞-idl : (f : Nat ⌞ 𝒟 ⌟) (ε∞ ⊗∞ f) ≡ f
⊗∞-idl f = funext λ x 𝒟.idl
⊗∞-idl f = funext λ x 𝒟.idl

⊗∞-idr : (f : Nat ⌞ 𝒟 ⌟) (f ⊗∞ ε∞) ≡ f
⊗∞-idr f = funext λ x 𝒟.idr
⊗∞-idr f = funext λ x 𝒟.idr

--------------------------------------------------------------------------------
-- Algebra
Expand All @@ -64,7 +64,7 @@ module Inf {o r} (𝒟 : Displacement-algebra o r) where
field
≤-everywhere : n f n 𝒟.≤ g n
<-somewhere : ∃[ n ∈ Nat ] (f n 𝒟.< g n)

open _inf<_ public

inf≤-everywhere : {f g} non-strict _inf<_ f g n f n 𝒟.≤ g n
Expand All @@ -78,7 +78,7 @@ module Inf {o r} (𝒟 : Displacement-algebra o r) where
inf<-trans f g h f<g g<h .≤-everywhere n = 𝒟.≤-trans (≤-everywhere f<g n) (≤-everywhere g<h n)
inf<-trans f g h f<g g<h .<-somewhere = ∥-∥-map (λ { (n , fn<gn) n , 𝒟.≤-transr fn<gn (≤-everywhere g<h n) }) (<-somewhere f<g)

inf<-is-prop : f g is-prop (f inf< g)
inf<-is-prop : f g is-prop (f inf< g)
inf<-is-prop f g f<g f<g′ i .≤-everywhere n = 𝒟.≤-thin (≤-everywhere f<g n) (≤-everywhere f<g′ n) i
inf<-is-prop f g f<g f<g′ i .<-somewhere = squash (<-somewhere f<g) (<-somewhere f<g′) i

Expand Down
56 changes: 28 additions & 28 deletions src/Mugen/Algebra/Displacement/NearlyConstant.agda
Original file line number Diff line number Diff line change
Expand Up @@ -95,15 +95,15 @@ module NearlyConst

-- Helper type for motives.
is-compact-case : {x base : ⌞ 𝒟 ⌟} Dec (x ≡ base) Type
is-compact-case p =
is-compact-case p =
Dec-elim _
(λ _ ⊥)
(λ _ ⊤)
p

-- Propositional computation helpers for 'is-compact'
¬base-is-compact : xs {x base} (x ≡ base ⊥) is-compact base (xs #r x)
¬base-is-compact xs {x = x} {base = base} ¬base with x ≡? base
¬base-is-compact xs {x = x} {base = base} ¬base with x ≡? base
... | yes base! = ¬base base!
... | no _ = tt

Expand Down Expand Up @@ -184,9 +184,9 @@ module NearlyConst

--------------------------------------------------------------------------------
-- Vanishing Lists
--
--
-- We say a list vanishes relative to some base 'b' if it /only/ contains 'b'.
-- Furthermore, we say a /backward/ list compacts relative to some base if
-- Furthermore, we say a /backward/ list compacts relative to some base if
-- it's compaction is equal to [].
--
-- These conditions may seems somewhat redundant. Why not define one as
Expand Down Expand Up @@ -247,14 +247,14 @@ module NearlyConst
compacts-head-∷ base x xs compacts =
vanish-head-∷ base x xs $
subst (vanishes base) (fwd-bwd (x ∷ xs)) $
vanishes-fwd base (bwd (x ∷ xs)) compacts
vanishes-fwd base (bwd (x ∷ xs)) compacts

compacts-tail-∷ : base x xs compact base (bwd (x ∷ xs)) ≡ [] compact base (bwd xs) ≡ []
compacts-tail-∷ base x xs compacts =
compacts-bwd base xs $
vanish-tail-∷ base x xs $
subst (vanishes base) (fwd-bwd (x ∷ xs)) $
vanishes-fwd base (bwd (x ∷ xs)) compacts
vanishes-fwd base (bwd (x ∷ xs)) compacts

compact-vanishr-++r : {base} xs ys compact base ys ≡ [] compact base (xs ++r ys) ≡ compact base xs
compact-vanishr-++r {base = base} xs [] ys-vanish = refl
Expand Down Expand Up @@ -316,7 +316,7 @@ module NearlyConst

--------------------------------------------------------------------------------
-- Merging Lists
--
--
-- We start by defining how to merge two lists without performing
-- compaction.

Expand Down Expand Up @@ -463,7 +463,7 @@ module NearlyConst
... | no ¬base =
refl

--------------------------------------------------------------------------------
-- Compact Support Lists
--
Expand Down Expand Up @@ -556,7 +556,7 @@ module NearlyConst
compact (xs .base) (xs .elts)
≡⟨ elts-compact xs ⟩
xs .elts ∎

-- Lifting of 'merge-assoc' to support lists.
merge-assoc : xs ys zs merge xs (merge ys zs) ≡ merge (merge xs ys) zs
merge-assoc xs ys zs = support-list-path 𝒟.associative $
Expand Down Expand Up @@ -704,19 +704,19 @@ module NearlyConst
... | lt _ = pf
... | eq _ = pf
... | gt y<x = lift (𝒟.<-irrefl (𝒟.≡-transl x≡y y<x))
merge-list≤-step≤ _ _ _ _ {x = x} {y = y} (inr x<y) pf with cmp x y
merge-list≤-step≤ _ _ _ _ {x = x} {y = y} (inr x<y) pf with cmp x y
... | lt _ = pf
... | eq _ = pf
... | gt y<x = lift (𝒟.<-asym x<y y<x)

merge-list<-step< : b1 xs b2 ys {x y} x < y merge-list≤ b1 xs b2 ys tri-rec (merge-list≤ b1 xs b2 ys) (merge-list< b1 xs b2 ys) (Lift _ ⊥) (cmp x y)
merge-list<-step< _ _ _ _ {x = x} {y = y} x<y pf with cmp x y
merge-list<-step< _ _ _ _ {x = x} {y = y} x<y pf with cmp x y
... | lt _ = pf
... | eq x≡y = absurd (𝒟.<-irrefl (𝒟.≡-transl (sym x≡y) x<y))
... | gt y<x = lift (𝒟.<-asym x<y y<x)

merge-list<-step≡ : b1 xs b2 ys {x y} x ≡ y merge-list< b1 xs b2 ys tri-rec (merge-list≤ b1 xs b2 ys) (merge-list< b1 xs b2 ys) (Lift _ ⊥) (cmp x y)
merge-list<-step≡ _ _ _ _ {x = x} {y = y} x≡y pf with cmp x y
merge-list<-step≡ _ _ _ _ {x = x} {y = y} x≡y pf with cmp x y
... | lt x<y = absurd (𝒟.<-irrefl (𝒟.≡-transl (sym x≡y) x<y))
... | eq _ = pf
... | gt y<x = lift (𝒟.<-irrefl (𝒟.≡-transl x≡y y<x))
Expand Down Expand Up @@ -847,20 +847,20 @@ module NearlyConst
... | lt x<b2 = merge-list<-step< b1 xs b3 [] (𝒟.<-trans x<b2 b2<b3) (go≤ xs [] [] xs<ys (inr b2<b3))
... | eq x≡b2 = merge-list<-step< b1 xs b3 [] (𝒟.≡-transl x≡b2 b2<b3) (go≤ xs [] [] (weaken-< b1 xs b2 [] xs<ys) (inr b2<b3))
go (x ∷ xs) [] (z ∷ zs) xs<ys ys<zs with cmp x b2 | cmp b2 z
... | lt x<b2 | lt b2<z = merge-list<-step< b1 xs b3 zs (𝒟.<-trans x<b2 b2<z) (go≤ xs [] zs xs<ys ys<zs)
... | lt x<b2 | eq b2≡z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transr x<b2 b2≡z) (go≤ xs [] zs xs<ys (weaken-< b2 [] b3 zs ys<zs))
... | eq x≡b2 | lt b2<z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transl x≡b2 b2<z) (go≤ xs [] zs (weaken-< b1 xs b2 [] xs<ys) ys<zs)
... | eq x≡b2 | eq b2≡z = merge-list<-step≡ b1 xs b3 zs (x≡b2 ∙ b2≡z) (go xs [] zs xs<ys ys<zs)
... | lt x<b2 | lt b2<z = merge-list<-step< b1 xs b3 zs (𝒟.<-trans x<b2 b2<z) (go≤ xs [] zs xs<ys ys<zs)
... | lt x<b2 | eq b2≡z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transr x<b2 b2≡z) (go≤ xs [] zs xs<ys (weaken-< b2 [] b3 zs ys<zs))
... | eq x≡b2 | lt b2<z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transl x≡b2 b2<z) (go≤ xs [] zs (weaken-< b1 xs b2 [] xs<ys) ys<zs)
... | eq x≡b2 | eq b2≡z = merge-list<-step≡ b1 xs b3 zs (x≡b2 ∙ b2≡z) (go xs [] zs xs<ys ys<zs)
go (x ∷ xs) (y ∷ ys) [] xs<ys ys<zs with cmp x y | cmp y b3
... | lt x<y | lt y<b3 = merge-list<-step< b1 xs b3 [] (𝒟.<-trans x<y y<b3) (go≤ xs ys [] xs<ys ys<zs)
... | lt x<y | eq y≡b3 = merge-list<-step< b1 xs b3 [] (𝒟.≡-transr x<y y≡b3) (go≤ xs ys [] xs<ys (weaken-< b2 ys b3 [] ys<zs))
... | eq x≡y | lt y<b3 = merge-list<-step< b1 xs b3 [] (𝒟.≡-transl x≡y y<b3) (go≤ xs ys [] (weaken-< b1 xs b2 ys xs<ys) ys<zs)
... | eq x≡y | eq y≡b3 = merge-list<-step≡ b1 xs b3 [] (x≡y ∙ y≡b3) (go xs ys [] xs<ys ys<zs)
... | lt x<y | lt y<b3 = merge-list<-step< b1 xs b3 [] (𝒟.<-trans x<y y<b3) (go≤ xs ys [] xs<ys ys<zs)
... | lt x<y | eq y≡b3 = merge-list<-step< b1 xs b3 [] (𝒟.≡-transr x<y y≡b3) (go≤ xs ys [] xs<ys (weaken-< b2 ys b3 [] ys<zs))
... | eq x≡y | lt y<b3 = merge-list<-step< b1 xs b3 [] (𝒟.≡-transl x≡y y<b3) (go≤ xs ys [] (weaken-< b1 xs b2 ys xs<ys) ys<zs)
... | eq x≡y | eq y≡b3 = merge-list<-step≡ b1 xs b3 [] (x≡y ∙ y≡b3) (go xs ys [] xs<ys ys<zs)
go (x ∷ xs) (y ∷ ys) (z ∷ zs) xs<ys ys<zs with cmp x y | cmp y z
... | lt x<y | lt y<z = merge-list<-step< b1 xs b3 zs (𝒟.<-trans x<y y<z) (go≤ xs ys zs xs<ys ys<zs)
... | lt x<y | eq y≡z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transr x<y y≡z) (go≤ xs ys zs xs<ys (weaken-< b2 ys b3 zs ys<zs))
... | eq x≡y | lt y<z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transl x≡y y<z) (go≤ xs ys zs (weaken-< b1 xs b2 ys xs<ys) ys<zs)
... | eq x≡y | eq y≡z = merge-list<-step≡ b1 xs b3 zs (x≡y ∙ y≡z) (go xs ys zs xs<ys ys<zs)
... | lt x<y | lt y<z = merge-list<-step< b1 xs b3 zs (𝒟.<-trans x<y y<z) (go≤ xs ys zs xs<ys ys<zs)
... | lt x<y | eq y≡z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transr x<y y≡z) (go≤ xs ys zs xs<ys (weaken-< b2 ys b3 zs ys<zs))
... | eq x≡y | lt y<z = merge-list<-step< b1 xs b3 zs (𝒟.≡-transl x≡y y<z) (go≤ xs ys zs (weaken-< b1 xs b2 ys xs<ys) ys<zs)
... | eq x≡y | eq y≡z = merge-list<-step≡ b1 xs b3 zs (x≡y ∙ y≡z) (go xs ys zs xs<ys ys<zs)

--------------------------------------------------------------------------------
-- Heterogenous Compositions
Expand Down Expand Up @@ -919,7 +919,7 @@ module NearlyConst
... | eq x≡b2 = step< xs [] [] (𝒟.≡-transl x≡b2 b2<b3) xs≤ys (inr b2<b3)
go (x ∷ xs) [] (z ∷ zs) xs≤ys ys<zs with cmp x b2 | cmp b2 z
... | lt x<b2 | lt b2<z = step< xs [] zs (𝒟.<-trans x<b2 b2<z) xs≤ys ys<zs
... | lt x<b2 | eq b2≡z = step< xs [] zs (𝒟.≡-transr x<b2 b2≡z) xs≤ys (weaken-< b2 [] b3 zs ys<zs)
... | lt x<b2 | eq b2≡z = step< xs [] zs (𝒟.≡-transr x<b2 b2≡z) xs≤ys (weaken-< b2 [] b3 zs ys<zs)
... | eq x≡b2 | lt b2<z = step< xs [] zs (𝒟.≡-transl x≡b2 b2<z) xs≤ys ys<zs
... | eq x≡b2 | eq b2≡z = step≤ xs [] zs (inl (x≡b2 ∙ b2≡z)) xs≤ys ys<zs
go (x ∷ xs) (y ∷ ys) [] xs≤ys ys<zs with cmp x y | cmp y b3
Expand Down Expand Up @@ -1041,7 +1041,7 @@ module NearlyConst
|> ⊎-mapl $ λ p
let ys≡[] : ys ≡ []
ys≡[] = bwd-inj $ ap elts (sym p)

b1≡b2 : b1 ≡ b2
b1≡b2 = ap base p

Expand All @@ -1055,7 +1055,7 @@ module NearlyConst
|> ⊎-mapl $ λ p
let xs≡[] : xs ≡ []
xs≡[] = bwd-inj $ ap elts p

b1≡b2 : b1 ≡ b2
b1≡b2 = ap base p

Expand Down Expand Up @@ -1299,7 +1299,7 @@ module NearlyConst
index b (fwd (compact b (([] #r x) ◁⊗ xs))) (suc n) ≡⟨ ap (λ ϕ index b (fwd (compact b ϕ)) (suc n)) (◁⊗-bwd ([] #r x) xs) ⟩
index b (fwd (compact b (([] #r x) ++r bwd xs))) (suc n) ≡⟨ ap (λ ϕ index b (fwd ϕ) (suc n)) (compact-++r ([] #r x) (bwd xs) (cs #r c) (p ∙ sym cs#r-compact)) ⟩
index b (fwd (compact b (([] #r x) ++r (cs #r c)))) (suc n) ≡⟨ ap (λ ϕ index b (fwd ϕ) (suc n)) (compact-done (([] #r x) ++r cs) c≠base) ⟩
index b (fwd ((([] #r x) ++r cs) #r c)) (suc n) ≡⟨ ap (λ ϕ index b ϕ (suc n)) (fwd-++r ([] #r x) (cs #r c)) ⟩
index b (fwd ((([] #r x) ++r cs) #r c)) (suc n) ≡⟨ ap (λ ϕ index b ϕ (suc n)) (fwd-++r ([] #r x) (cs #r c)) ⟩
index b (fwd (cs #r c)) n ≡˘⟨ ap (λ ϕ index b (fwd ϕ) n) p ⟩
index b (fwd (compact b (bwd xs))) n ≡⟨ index-compact b xs n ⟩
index b xs n ∎
Expand Down
2 changes: 1 addition & 1 deletion src/Mugen/Algebra/Displacement/NonPositive.agda
Original file line number Diff line number Diff line change
Expand Up @@ -49,7 +49,7 @@ NonPositive+⊆Int+ = to-displacement-subalgebra subalg where
subalg : make-displacement-subalgebra NonPositive+ Int+
subalg .make-displacement-subalgebra.into x = - x
subalg .make-displacement-subalgebra.pres-ε = refl
subalg .make-displacement-subalgebra.pres-⊗ = +ℤ-negate
subalg .make-displacement-subalgebra.pres-⊗ = +ℤ-negate
subalg .make-displacement-subalgebra.strictly-mono x y = negate-anti-mono y x
subalg .make-displacement-subalgebra.inj = negate-inj _ _

Expand Down
2 changes: 1 addition & 1 deletion src/Mugen/Algebra/Displacement/Product.agda
Original file line number Diff line number Diff line change
Expand Up @@ -163,7 +163,7 @@ module ProductProperties {o r} {𝒟₁ 𝒟₂ : Displacement-algebra o r}

⊗×-right-invariant : x y z x ⊗×≤ y (x ⊗× z) ⊗×≤ (y ⊗× z)
⊗×-right-invariant x y z (both≤ x1≤y1 x2≤y2) = both≤ (𝒟₁-ordered-monoid.right-invariant x1≤y1) (𝒟₂-ordered-monoid.right-invariant x2≤y2)

--------------------------------------------------------------------------------
-- Joins

Expand Down
4 changes: 2 additions & 2 deletions src/Mugen/Algebra/OrderedMonoid.agda
Original file line number Diff line number Diff line change
Expand Up @@ -29,14 +29,14 @@ record is-ordered-monoid
field
has-is-monoid : is-monoid ε _⊗_
invariant : {w x y z} w ≤ y x ≤ z (w ⊗ x) ≤ (y ⊗ z)

open is-monoid has-is-monoid public

left-invariant : {x y z} y ≤ z (x ⊗ y) ≤ (x ⊗ z)
left-invariant y≤z = invariant ≤-refl y≤z

right-invariant : {x y z} x ≤ y (x ⊗ z) ≤ (y ⊗ z)
right-invariant x≤y = invariant x≤y ≤-refl
right-invariant x≤y = invariant x≤y ≤-refl

record Ordered-monoid-on {o r : Level} (A : Poset o r) : Type (o ⊔ lsuc r) where
field
Expand Down
2 changes: 1 addition & 1 deletion src/Mugen/Cat/HierarchyTheory/Properties.agda
Original file line number Diff line number Diff line change
Expand Up @@ -91,7 +91,7 @@ module _ {o r} (H : Hierarchy-theory o r) (Δ : Strict-order o r) (Ψ : Set (lsu
ι₁-monic g h p = ext λ α
inl-inj (inr-inj (p #ₚ α))


--------------------------------------------------------------------------------
-- Construction of the functor T
-- Section 3.4, Lemma 3.8
Expand Down
4 changes: 2 additions & 2 deletions src/Mugen/Data/Coimage.agda
Original file line number Diff line number Diff line change
Expand Up @@ -127,7 +127,7 @@ Coim-map₂ : ∀ {f : A → B}
Coim f Coim f Coim f
Coim-map₂ h h-pres = Coim-rec₂ squash
(λ x y inc (h x y))
(λ w x y z p q glue (h w y) (h x z) (h-pres w x y z p q))
(λ w x y z p q glue (h w y) (h x z) (h-pres w x y z p q))


module Coim-Path (f : A B) (B-set : is-set B) where
Expand Down Expand Up @@ -157,4 +157,4 @@ module Coim-Path (f : A → B) (B-set : is-set B) where

Coim-effectful : {x y} Path (Coim f) (inc x) (inc y) f x ≡ f y
Coim-effectful = Coim-path

6 changes: 3 additions & 3 deletions src/Mugen/Data/Int.agda
Original file line number Diff line number Diff line change
Expand Up @@ -336,8 +336,8 @@ diff-negsuc-< zero zero = tt
diff-negsuc-< zero (suc y) = <-suc y
diff-negsuc-< (suc x) zero = tt
diff-negsuc-< (suc x) (suc y) = begin-<
negsuc (suc y) <⟨ -1ℤ-< (negsuc y) ⟩
negsuc y <⟨ diff-negsuc-< x y ⟩
negsuc (suc y) <⟨ -1ℤ-< (negsuc y) ⟩
negsuc y <⟨ diff-negsuc-< x y ⟩
diff x y <∎

diff-left-invariant : x y z z < y diff x y <ℤ diff x z
Expand Down Expand Up @@ -425,7 +425,7 @@ negate-anti-mono (suc x) (suc y) (s≤s x<y) = x<y

ℤ-Strict-order : Strict-order lzero lzero
ℤ-Strict-order = to-strict-order mk where
mk : make-strict-order _ _
mk : make-strict-order _ _
mk .make-strict-order._<_ = _<ℤ_
mk .make-strict-order.<-irrefl = <ℤ-irrefl _
mk .make-strict-order.<-trans = <ℤ-trans _ _ _
Expand Down
6 changes: 3 additions & 3 deletions src/Mugen/Data/List.agda
Original file line number Diff line number Diff line change
Expand Up @@ -22,7 +22,7 @@ module _ {ℓ} {A : Type ℓ} (aset : is-set A) where

++-is-magma : is-magma {A = List A} _++_
++-is-magma .has-is-set = ListPath.List-is-hlevel 0 aset

++-is-semigroup : is-semigroup {A = List A} _++_
++-is-semigroup .has-is-magma = ++-is-magma
++-is-semigroup .associative {x} {y} {z} = sym (++-assoc x y z)
Expand Down Expand Up @@ -69,7 +69,7 @@ replicater (suc n) a = replicater n a #r a
-- Left action of backwards lists upon lists.
_⊗▷_ : Bwd A List A List A
[] ⊗▷ ys = ys
(xs #r x) ⊗▷ ys = xs ⊗▷ (x ∷ ys)
(xs #r x) ⊗▷ ys = xs ⊗▷ (x ∷ ys)

-- Right action of lists upon backwards lists.
_◁⊗_ : Bwd A List A Bwd A
Expand Down Expand Up @@ -182,7 +182,7 @@ Bwd-is-hlevel n ahl = is-hlevel≃ (2 + n) Bwd≃List (List-is-hlevel n ahl)

instance
H-Level-Bwd : {n} {k} ⦃ H-Level A (2 + n) ⦄ H-Level (Bwd A) (2 + n + k)
H-Level-Bwd {n = n} ⦃ x ⦄ =
H-Level-Bwd {n = n} ⦃ x ⦄ =
basic-instance (2 + n) (Bwd-is-hlevel n (H-Level.has-hlevel x))


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