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appease the whitespace gods
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Cubical/Algebra/Heap/Properties.agda

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@@ -92,14 +92,14 @@ StructureGroup H = toldYaSo inhab module StructureGroup where
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φ : e e' GroupHom (fromPoint e) (fromPoint e')
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φ e e' .fst x = [ e' , e , x ]
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φ e e' .snd = makeIsGroupHom λ x y
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φ e e' .snd = makeIsGroupHom λ x y
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[ e' , e , [ x , e , y ] ] ≡⟨ assoc e' e x e y ⟩
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[ [ e' , e , x ] , e , y ] ≡⟨ cong [ [ e' , e , x ] ,_, y ] (sym (idr e e')) ⟩
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[ [ e' , e , x ] , [ e , e' , e' ] , y ] ≡⟨ assocr [ e' , e , x ] e' e' e y ⟩
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[ [ e' , e , x ] , e' , [ e' , e , y ] ] ∎
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φ-coh : e e' e'' x φ e' e'' .fst (φ e e' .fst x) ≡ φ e e'' .fst x
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φ-coh e e' e'' x =
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φ-coh e e' e'' x =
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[ e'' , e' , [ e' , e , x ] ] ≡⟨ sym (assocr e'' e' e' e x) ⟩
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[ e'' , [ e , e' , e' ] , x ] ≡⟨ cong [ e'' ,_, x ] (idr e e') ⟩
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[ e'' , e , x ] ∎
@@ -141,7 +141,7 @@ PointedHeap≡ eqv p = cong₂ _,_ (uaHeap eqv) (ua-gluePath _ p)
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GroupsArePointedHeaps : Group ℓ ≃ PointedHeap ℓ
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GroupsArePointedHeaps {ℓ} = isoToEquiv asIso module GroupsArePointedHeaps where
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open Iso
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asIso : Iso (Group ℓ) (PointedHeap ℓ)
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asIso .fun G = GroupHeap G , G .snd .GroupStr.1g
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asIso .inv (H , e) = StructureGroup.fromPoint H e

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