comp_ofBijective_symm — Mathlib

English

If f is a bijective nonunital ring hom, then f.comp((RingEquiv.ofBijective f hf).symm) = id on S.

Русский

Если f биективный нена единичный кольцевой гомоморфизм, то f ∘ (RingEquiv.ofBijective f hf).symm = id_S.

LaTeX

$$$f \\circ (\\mathrm{RingEquiv.ofBijective}(f, hf).symm) = \\mathrm{id}_S$$$

Lean4

@[simp]
theorem comp_ofBijective_symm (f : R →ₙ+* S) (hf : Function.Bijective f) :
    f.comp ((RingEquiv.ofBijective f hf).symm : _ →ₙ+* _) = NonUnitalRingHom.id S :=
  by
  ext
  exact (RingEquiv.ofBijective f hf).symm.injective <| RingEquiv.apply_symm_apply ..

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