fst_compl — Mathlib

English

In a product α × β with HasCompl on each component, the first projection of aᶜ equals the complement of the first projection: aᶜ₁ = (a₁)ᶜ.

Русский

В произведении α × β с/complement на каждой компоненте, первая проекция aᶜ равна комплементу первой проекции: aᶜ₁ = (a₁)ᶜ.

LaTeX

$$$ a^\complement_1 = a_1^\complement $$$

Lean4

@[simp]
theorem fst_compl [HasCompl α] [HasCompl β] (a : α × β) : aᶜ.1 = a.1ᶜ :=
  rfl

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