snd_apply_inr — Mathlib

English

The map toProd comp inl equals inl, and comp inr equals inr; i.e., (toProd ∘ inl) = inl and (toProd ∘ inr) = inr.

Русский

Отображение toProd с inl даёт inl, с inr даёт inr; то есть (toProd ∘ inl) = inl и (toProd ∘ inr) = inr.

LaTeX

$$$(\\\\mathrm{toProd} \\\\circ \\\\mathrm{inl}) = \\\\mathrm{inl}, \quad (\\\\mathrm{toProd} \\\\circ \\\\mathrm{inr}) = \\\\mathrm{inr}.$$$

Lean4

@[to_additive (attr := simp)]
theorem snd_apply_inr (x : N) : snd (inr x : M ∗ N) = x :=
  rfl

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