lTensor_shortComplex_exact — Mathlib

English

If reg is IsSMulRegular R x, then reg is IsSMulRegular S (algebraMap R S x).

Русский

Если рег = IsSMulRegular R x, то рег = IsSMulRegular S (algebraMap R S x).

LaTeX

$$$\\forall x,\\; IsSMulRegular R x \\Rightarrow IsSMulRegular S (algebraMap R S x)$$$

Lean4

theorem lTensor_shortComplex_exact [Flat R M] (C : ShortComplex <| ModuleCat R) (hC : C.Exact) :
    C.map (tensorLeft M) |>.Exact :=
  by
  rw [moduleCat_exact_iff_function_exact] at hC ⊢
  exact lTensor_exact M hC

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