refactor: Some replacement with rfl
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5 changed files with 12 additions and 22 deletions
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@ -56,14 +56,10 @@ def toEquiv (m : f ⟶ g) : f.left ≃ g.left where
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@[simp]
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lemma toEquiv_id (f : OverColor C) : toEquiv (𝟙 f) = Equiv.refl f.left := by
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ext x
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simp only [toEquiv, Equiv.coe_fn_mk, Equiv.refl_apply]
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rfl
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@[simp]
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lemma toEquiv_comp (m : f ⟶ g) (n : g ⟶ h) : toEquiv (m ≫ n) = (toEquiv m).trans (toEquiv n) := by
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ext x
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simp only [toEquiv, Equiv.coe_fn_mk, Equiv.trans_apply]
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rfl
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lemma toEquiv_symm_apply (m : f ⟶ g) (i : g.left) :
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@ -489,7 +489,6 @@ def obj' : MonoidalFunctor (OverColor C) (Rep k G) where
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simp only [discreteFunctorMapEqIso, Functor.mapIso_hom, eqToIso.hom, Functor.mapIso_inv,
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eqToIso.inv, LinearEquiv.ofLinear_apply]
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rw [discreteFun_hom_trans]
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apply congrArg
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rfl
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μ_natural_left := μ_natural_left F
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μ_natural_right := μ_natural_right F
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@ -672,7 +671,7 @@ lemma μIso_inv_tprod (F : Discrete C ⥤ Rep k G) (X Y : OverColor C)
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change ((Action.forget _ _).mapIso ((lift.obj F).μIso X Y)).inv (PiTensorProduct.tprod k p) = _
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trans ((Action.forget _ _).mapIso ((lift.obj F).μIso X Y)).toLinearEquiv.symm
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(PiTensorProduct.tprod k p)
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· congr
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· rfl
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erw [← LinearEquiv.eq_symm_apply]
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change _ = ((lift.obj F).μ X Y).hom _
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erw [obj_μ_tprod_tmul]
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@ -710,8 +709,7 @@ def forgetLiftAppV (c : C) : ((lift.obj F).obj (OverColor.mk (fun (_ : Fin 1) =>
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@[simp]
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lemma forgetLiftAppV_symm_apply (c : C) (x : (F.obj (Discrete.mk c)).V) :
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(forgetLiftAppV F c).symm x = PiTensorProduct.tprod k (fun _ => x) := by
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simp only [forgetLiftAppV, Fin.isValue, Functor.id_obj]
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erw [PiTensorProduct.subsingletonEquiv_symm_apply]
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rfl
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/-- The `forgetLiftAppV` function takes an object `c` of type `C` and returns a isomorphism
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between the objects obtained by applying the lift of `F` and that obtained by applying
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