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lines changed Original file line number Diff line number Diff line change @@ -291,19 +291,19 @@ lemma compr₂_linearEquiv (ist : IsTensorProduct f) (e : M ≃ₗ[R] M') :
291291 rw [TensorProduct.lift_compr₂]
292292 exact e.bijective.comp ist
293293
294- lemma comp_compl₂_linearEquiv (ist : IsTensorProduct f) (e₁ : N₁ ≃ₗ[R] M₁) (e₂ : N₂ ≃ₗ[R] M₂) :
294+ lemma compl₂_comp_linearEquiv (ist : IsTensorProduct f) (e₁ : N₁ ≃ₗ[R] M₁) (e₂ : N₂ ≃ₗ[R] M₂) :
295295 IsTensorProduct ((f.comp e₁.toLinearMap).compl₂ e₂.toLinearMap):= by
296296 simp only [IsTensorProduct] at ist ⊢
297297 rw [← TensorProduct.lift_comp_map, ← LinearMap.rTensor_comp_lTensor]
298298 exact ist.comp ((e₁.rTensor M₂).bijective.comp (e₂.lTensor N₁).bijective)
299299
300300lemma comp_linearEquiv (ist : IsTensorProduct f) (e₁ : N₁ ≃ₗ[R] M₁) :
301301 IsTensorProduct (f.comp e₁.toLinearMap) :=
302- ist.comp_compl₂_linearEquiv e₁ (LinearEquiv.refl R M₂)
302+ ist.compl₂_comp_linearEquiv e₁ (LinearEquiv.refl R M₂)
303303
304304lemma compl₂_linearEquiv (ist : IsTensorProduct f) (e₂ : N₂ ≃ₗ[R] M₂) :
305305 IsTensorProduct (f.compl₂ e₂.toLinearMap) :=
306- ist.comp_compl₂_linearEquiv (LinearEquiv.refl R M₁) e₂
306+ ist.compl₂_comp_linearEquiv (LinearEquiv.refl R M₁) e₂
307307
308308end
309309
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