sumElim_right — Mathlib

English

There is a homeomorphism between (Sum X Y) × Z and Sum (X × Z) (Y × Z): the order of taking product with Z can be distributed over the sum.

Русский

Существует гомеоморфизм между (Sum X Y) × Z и Sum (X × Z) (Y × Z): произведение можно распределить над суммой.

LaTeX

$$$ (X \\oplus Y) \\times Z \\cong_T (X \\times Z) \\oplus (Y \\times Z) $$$

Lean4

/-- If `Sum.elim f g` is an inducing map, then so is `g`. -/
theorem sumElim_right (h : IsInducing (Sum.elim f g)) : IsInducing g :=
  elim_comp_inr f g ▸ h.comp IsEmbedding.inr.isInducing

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