prod_univ_seven — Mathlib

English

For any f: Fin 7 → M, the product equals f(0) f(1) f(2) f(3) f(4) f(5) f(6).

Русский

Для любого f: Fin 7 → M произведение равно f(0) f(1) f(2) f(3) f(4) f(5) f(6).

LaTeX

$$$\displaystyle \prod_{i \in \mathrm{Fin}(7)} f(i) = f(0) \cdot f(1) \cdot f(2) \cdot f(3) \cdot f(4) \cdot f(5) \cdot f(6).$$$

Lean4

@[to_additive]
theorem prod_univ_seven (f : Fin 7 → M) : ∏ i, f i = f 0 * f 1 * f 2 * f 3 * f 4 * f 5 * f 6 :=
  by
  rw [prod_univ_castSucc, prod_univ_six]
  rfl

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