zeta_prod_apply — Mathlib

English

For pairs (a1,b1) and (a2,b2) in α×β, zeta on the product equals the product of the zetas on components: zeta 𝕜 (a1,b1) (a2,b2) = zeta 𝕜 a1 a2 · zeta 𝕜 b1 b2.

Русский

На произведении позитива: zeta на паре (a1,b1) (a2,b2) равна произведению zeta на компонентах: zeta 𝕜 (a1,b1) (a2,b2) = zeta 𝕜 a1 a2 · zeta 𝕜 b1 b2.

LaTeX

$$$ zeta 𝕜 (a_1,b_1) (a_2,b_2) = zeta 𝕜 a_1 a_2 \cdot zeta 𝕜 b_1 b_2 $$$

Lean4

theorem zeta_prod_apply (a b : α × β) : zeta 𝕜 a b = zeta 𝕜 a.1 b.1 * zeta 𝕜 a.2 b.2 := by
  simp [← ite_and, Prod.le_def, and_comm]

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