baseChangeAux_surj — Mathlib

English

A nonrecursive induction principle for finitely presented ring maps with polynomial base and closure under composition.

Русский

Нестационное основание индукции FP-гомоморфизмов с многочленами и замыкание по композиции.

LaTeX

$$$\\text{Induction principle for FP maps with polynomial base and closure under composition}$$$

Lean4

theorem baseChangeAux_surj {σ : Type*} {f : MvPolynomial σ R →ₐ[R] A} (hf : Function.Surjective f) :
    Function.Surjective (Algebra.TensorProduct.map (AlgHom.id B B) f) :=
  by
  change Function.Surjective (TensorProduct.map (AlgHom.id R B) f)
  apply TensorProduct.map_surjective
  · exact Function.RightInverse.surjective (congrFun rfl)
  · exact hf

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