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fix naming
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Mathlib/RingTheory/IsTensorProduct.lean

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@@ -291,19 +291,19 @@ lemma compr₂_linearEquiv (ist : IsTensorProduct f) (e : M ≃ₗ[R] M') :
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rw [TensorProduct.lift_compr₂]
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exact e.bijective.comp ist
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lemma comp_compl₂_linearEquiv (ist : IsTensorProduct f) (e₁ : N₁ ≃ₗ[R] M₁) (e₂ : N₂ ≃ₗ[R] M₂) :
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lemma compl₂_comp_linearEquiv (ist : IsTensorProduct f) (e₁ : N₁ ≃ₗ[R] M₁) (e₂ : N₂ ≃ₗ[R] M₂) :
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IsTensorProduct ((f.comp e₁.toLinearMap).compl₂ e₂.toLinearMap):= by
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simp only [IsTensorProduct] at ist ⊢
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rw [← TensorProduct.lift_comp_map, ← LinearMap.rTensor_comp_lTensor]
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exact ist.comp ((e₁.rTensor M₂).bijective.comp (e₂.lTensor N₁).bijective)
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lemma comp_linearEquiv (ist : IsTensorProduct f) (e₁ : N₁ ≃ₗ[R] M₁) :
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IsTensorProduct (f.comp e₁.toLinearMap) :=
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ist.comp_compl₂_linearEquiv e₁ (LinearEquiv.refl R M₂)
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ist.compl₂_comp_linearEquiv e₁ (LinearEquiv.refl R M₂)
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lemma compl₂_linearEquiv (ist : IsTensorProduct f) (e₂ : N₂ ≃ₗ[R] M₂) :
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IsTensorProduct (f.compl₂ e₂.toLinearMap) :=
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ist.comp_compl₂_linearEquiv (LinearEquiv.refl R M₁) e₂
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ist.compl₂_comp_linearEquiv (LinearEquiv.refl R M₁) e₂
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end
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