mkAlgHom_surjective — Mathlib

English

The surjectivity of mkAlgHom S s holds: every element of RingQuot s is the image of some element of A under mkAlgHom.

Русский

Сюръективность mkAlgHom S s (повтор): каждый элемент RingQuot s является образом некоторого элемента A.

LaTeX

$$∀ y:\\, RingQuot s, ∃ a:\\, A, mkAlgHom S s a = y$$

Lean4

theorem mkAlgHom_surjective (s : A → A → Prop) : Function.Surjective (mkAlgHom S s) :=
  by
  suffices Function.Surjective fun x ↦ (⟨.mk (Rel s) x⟩ : RingQuot s) by simpa [mkAlgHom_def, mkRingHom_def]
  rintro ⟨⟨a⟩⟩
  use a

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