sumElim_left — Mathlib

English

The map X × (Y ⊕ Z) → (X × Y) ⊕ (X × Z) is a homeomorphism, built from swapping the factors and distributing across the sum.

Русский

Гомеоморфизм между X × (Y ⊕ Z) и (X × Y) ⊕ (X × Z) строится через обмен фактор и распределение по сумме.

LaTeX

$$$ \\mathrm{ProdSumDistrib}: X \\times (Y \\oplus Z) \\xrightarrow{\\cong_T} (X \\times Y) \\oplus (X \\times Z) $$$

Lean4

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

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