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chore: remove duplicated MulDistribMulAction instances #866

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Merged
kbuzzard merged 1 commit into from
Feb 26, 2026
Merged

chore: remove duplicated MulDistribMulAction instances #866

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34 changes: 0 additions & 34 deletions FLT/Deformations/RepresentationTheory/Etale.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -478,37 +478,3 @@ instance {A : Type*} [CommRing A] [Bialgebra K A] :
change r (algebraMap _ _ _) = _
simp
rfl

noncomputable
instance {A : Type*} [CommRing A] [Bialgebra K A] :
MulDistribMulAction (L ≃ₐ[K] L) (A →ₐ[K] L) where
smul_mul r f g := by
ext x
change r (Algebra.TensorProduct.lift _ _ (fun _ _ ↦ .all _ _) (Coalgebra.comul x)) =
Algebra.TensorProduct.lift _ _ (fun _ _ ↦ .all _ _) (Coalgebra.comul x)
induction Coalgebra.comul (R := K) x with
| zero => simp only [map_zero]
| add x y _ _ => simp only [map_add, *]
| tmul x y => simp; rfl
smul_one r := by
ext x
change r (algebraMap _ _ _) = _
simp
rfl

noncomputable
instance {A : Type*} [CommRing A] [Bialgebra K A] :
MulDistribMulAction (L ≃ₐ[K] L) (A →ₐ[K] L) where
smul_mul r f g := by
ext x
change r (Algebra.TensorProduct.lift _ _ (fun _ _ ↦ .all _ _) (Coalgebra.comul x)) =
Algebra.TensorProduct.lift _ _ (fun _ _ ↦ .all _ _) (Coalgebra.comul x)
induction Coalgebra.comul (R := K) x with
| zero => simp only [map_zero]
| add x y _ _ => simp only [map_add, *]
| tmul x y => simp; rfl
smul_one r := by
ext x
change r (algebraMap _ _ _) = _
simp
rfl