refactor: Some replacement with rfl

This commit is contained in:
jstoobysmith 2024-10-19 10:34:30 +00:00
parent 48bec8c891
commit 3e1cd363bd
5 changed files with 12 additions and 22 deletions

View file

@ -56,14 +56,10 @@ def toEquiv (m : f ⟶ g) : f.left ≃ g.left where
@[simp]
lemma toEquiv_id (f : OverColor C) : toEquiv (𝟙 f) = Equiv.refl f.left := by
ext x
simp only [toEquiv, Equiv.coe_fn_mk, Equiv.refl_apply]
rfl
@[simp]
lemma toEquiv_comp (m : f ⟶ g) (n : g ⟶ h) : toEquiv (m ≫ n) = (toEquiv m).trans (toEquiv n) := by
ext x
simp only [toEquiv, Equiv.coe_fn_mk, Equiv.trans_apply]
rfl
lemma toEquiv_symm_apply (m : f ⟶ g) (i : g.left) :

View file

@ -489,7 +489,6 @@ def obj' : MonoidalFunctor (OverColor C) (Rep k G) where
simp only [discreteFunctorMapEqIso, Functor.mapIso_hom, eqToIso.hom, Functor.mapIso_inv,
eqToIso.inv, LinearEquiv.ofLinear_apply]
rw [discreteFun_hom_trans]
apply congrArg
rfl
μ_natural_left := μ_natural_left F
μ_natural_right := μ_natural_right F
@ -672,7 +671,7 @@ lemma μIso_inv_tprod (F : Discrete C ⥤ Rep k G) (X Y : OverColor C)
change ((Action.forget _ _).mapIso ((lift.obj F).μIso X Y)).inv (PiTensorProduct.tprod k p) = _
trans ((Action.forget _ _).mapIso ((lift.obj F).μIso X Y)).toLinearEquiv.symm
(PiTensorProduct.tprod k p)
· congr
· rfl
erw [← LinearEquiv.eq_symm_apply]
change _ = ((lift.obj F).μ X Y).hom _
erw [obj_μ_tprod_tmul]
@ -710,8 +709,7 @@ def forgetLiftAppV (c : C) : ((lift.obj F).obj (OverColor.mk (fun (_ : Fin 1) =>
@[simp]
lemma forgetLiftAppV_symm_apply (c : C) (x : (F.obj (Discrete.mk c)).V) :
(forgetLiftAppV F c).symm x = PiTensorProduct.tprod k (fun _ => x) := by
simp only [forgetLiftAppV, Fin.isValue, Functor.id_obj]
erw [PiTensorProduct.subsingletonEquiv_symm_apply]
rfl
/-- The `forgetLiftAppV` function takes an object `c` of type `C` and returns a isomorphism
between the objects obtained by applying the lift of `F` and that obtained by applying