@@ -98,37 +98,20 @@ module Initial {x xℓ} where
9898 sym : Symmetric _≈_
9999 sym {x = ()}
100100
101- trans : Transitive _≈_
102- trans {i = ()}
103-
104101 module _ {f} {F : Set f} where
105102
106103 infix 7 ❲_❳⤙_⤚_
107104 ❲_❳⤙_⤚_ : Op₃ₗ F Carrier
108105 ❲_❳⤙_⤚_ _ ()
109106
110- module _ {fℓ} (_≈ᶠ_ : Rel F fℓ) where
111- private
112- module L = LeftDefs ❲_❳⤙_⤚_ _≈_
113-
114- ❲❳⤙⤚-cong : L.Congruent₃ _≈ᶠ_
115- ❲❳⤙⤚-cong {u = ()}
116-
117107 infix 7 _⤙_⤚❲_❳
118108 _⤙_⤚❲_❳ : Op₃ᵣ F Carrier
119109 _⤙_⤚❲_❳ ()
120110
121- module _ {fℓ} (_≈ᶠ_ : Rel F fℓ) where
122- private
123- module R = RightDefs _⤙_⤚❲_❳ _≈_
124-
125- ⤙⤚❲❳-cong : R.Congruent₃ _≈ᶠ_
126- ⤙⤚❲❳-cong {x = ()}
127-
128111 open ℤero
129112
130113 isEquivalence : IsEquivalence _≈_
131- isEquivalence = record { ℤero }
114+ isEquivalence = record { ℤero; trans = λ {i = i} → ⊥-elim i }
132115
133116 module _ {f fℓ} (F : AlmostFumula f fℓ) where
134117
@@ -139,7 +122,7 @@ module Initial {x xℓ} where
139122 ; ❲_❳⤙_⤚_ = ❲_❳⤙_⤚_
140123 ; isLeftAlmostFumulaExtrusion = record
141124 { isEquivalence = isEquivalence
142- ; ❲❳⤙⤚-cong = ❲❳⤙⤚-cong (AlmostFumula._≈_ F)
125+ ; ❲❳⤙⤚-cong = λ {u = u} → ⊥-elim u
143126 ; ❲❳⤙⤚-double-exchange = λ _ ()
144127 }
145128 }
@@ -153,7 +136,7 @@ module Initial {x xℓ} where
153136 ; _⤙_⤚❲_❳ = _⤙_⤚❲_❳
154137 ; isRightAlmostFumulaExtrusion = record
155138 { isEquivalence = isEquivalence
156- ; ⤙⤚❲❳-cong = ⤙⤚❲❳-cong (AlmostFumula._≈_ F)
139+ ; ⤙⤚❲❳-cong = λ {x = x} → ⊥-elim x
157140 ; ⤙⤚❲❳-double-exchange = λ ()
158141 }
159142 }
@@ -170,9 +153,9 @@ module Initial {x xℓ} where
170153 ; _⤙_⤚❲_❳ = _⤙_⤚❲_❳
171154 ; isDoubleAlmostFumulaExtrusion = record
172155 { isEquivalence = isEquivalence
173- ; ❲❳⤙⤚-cong = ❲❳⤙⤚-cong (AlmostFumula._≈_ Fₗ)
156+ ; ❲❳⤙⤚-cong = λ {u = u} → ⊥-elim u
174157 ; ❲❳⤙⤚-double-exchange = λ _ ()
175- ; ⤙⤚❲❳-cong = ⤙⤚❲❳-cong (AlmostFumula._≈_ Fᵣ)
158+ ; ⤙⤚❲❳-cong = λ {x = x} → ⊥-elim x
176159 ; ⤙⤚❲❳-double-exchange = λ ()
177160 ; ❲❳⤙⤚-⤙⤚❲❳-double-exchange = λ _ ()
178161 }
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