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chore(AlgebraicTopology/Reedy): cosmetic cleanups (leanprover-community#41581)
This PR makes three cosmetic fixes in `Mathlib/AlgebraicTopology/Reedy/Basic.lean`: replace the ASCII `<-` with `←` in the proof of `degHom_comp_le_right`, fix the grammar typo "degree of a morphisms" in the docstring of `degHom`, and delete the unused `universe u` declaration. Follow-up to [leanprover-community#41141 (feat(AlgebraicTopology): Reedy structures)](leanprover-community#41141). 🤖 Prepared with Claude Code
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Mathlib/AlgebraicTopology/Reedy/Basic.lean

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@@ -30,8 +30,6 @@ https://github.com/leanprover-community/project-intentions/issues/5
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@[expose] public section
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universe u
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open CategoryTheory
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namespace HomotopicalAlgebra
@@ -123,7 +121,7 @@ lemma unique {X Y : C} {f : X ⟶ Y} (fac fac' : W₁.MapFactorizationData W₂
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obtain rfl : fac = fac' := Subsingleton.elim _ _
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simp
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/-- The degree of a morphisms for a Reedy structure. It is defined as the degree of
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/-- The degree of a morphism for a Reedy structure. It is defined as the degree of
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the intermediate object in the Reedy factorization, but it is also the smallest
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degree of an intermediate object in a factorization, see the lemma `degHom_le`. -/
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@[no_expose]
@@ -168,7 +166,7 @@ lemma degHom_comp_le_left {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) :
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lemma degHom_comp_le_right {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) :
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r.degHom (f ≫ g) ≤ r.degHom g := by
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have ⟨_, g₁, g₂, _, _, h_fac, h_deg⟩ := r.exists_fac g
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rw [h_deg, ← h_fac, <- Category.assoc]
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rw [h_deg, ← h_fac, Category.assoc]
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exact r.degHom_le (f ≫ g₁) g₂
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lemma prop₂_of_degHom_eq_deg_left {X Y : C} {f : X ⟶ Y} (hf : r.degHom f = r.deg X) :

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