Finrank tensor Product adic Completion eq finrank pi adic Completion

lemma finrank_tensorProduct_adicCompletion_eq_finrank_pi_adicCompletion :    Module.finrank (adicCompletion K v) (L ⊗[K] adicCompletion K v) =      Module.finrank (adicCompletion K v) ((w : Extension B v) → adicCompletion L w.val) :=  letI := Extension.fintype A K L B v  calc Module.finrank (adicCompletion K v) (L ⊗[K] adicCompletion K v)    _ = Module.finrank K L := by rw [TensorProduct.finrank_rightAlgebra]    _ = ∑ (w : Extension B v), Ideal.ramificationIdx' v.asIdeal w.val.asIdeal *        Ideal.inertiaDeg' v.asIdeal w.val.asIdeal := by        rw [Ideal.sum_ramification_inertia_extensions]    _ = ∑ (w : Extension B v), Module.finrank (adicCompletion K v) (adicCompletion L w.val) :=        Finset.sum_congr rfl fun w _ ↦ ramificationIdx_mul_inertiaDeg_eq_finrank K L w    _ = Module.finrank (adicCompletion K v) ((w : Extension B v) → adicCompletion L w.val) := by        rw [Module.finrank_pi_fintype (adicCompletion K v)]