diff --git a/Mathlib/Algebra/BigOperators/Fin.lean b/Mathlib/Algebra/BigOperators/Fin.lean index 2a445b2244dcc..5e74ef85d66a6 100644 --- a/Mathlib/Algebra/BigOperators/Fin.lean +++ b/Mathlib/Algebra/BigOperators/Fin.lean @@ -55,7 +55,7 @@ theorem prod_univ_zero [CommMonoid β] (f : Fin 0 → β) : ∏ i, f i = 1 := /-- A product of a function `f : Fin (n + 1) → β` over all `Fin (n + 1)` is the product of `f x`, for some `x : Fin (n + 1)` times the remaining product -/ @[to_additive "A sum of a function `f : Fin (n + 1) → β` over all `Fin (n + 1)` is the sum of -`f x`, for some `x : Fin (n + 1)` plus the remaining product"] +`f x`, for some `x : Fin (n + 1)` plus the remaining sum"] theorem prod_univ_succAbove [CommMonoid β] {n : ℕ} (f : Fin (n + 1) → β) (x : Fin (n + 1)) : ∏ i, f i = f x * ∏ i : Fin n, f (x.succAbove i) := by rw [univ_succAbove, prod_cons, Finset.prod_map _ x.succAboveEmb] @@ -64,7 +64,7 @@ theorem prod_univ_succAbove [CommMonoid β] {n : ℕ} (f : Fin (n + 1) → β) ( /-- A product of a function `f : Fin (n + 1) → β` over all `Fin (n + 1)` is the product of `f 0` plus the remaining product -/ @[to_additive "A sum of a function `f : Fin (n + 1) → β` over all `Fin (n + 1)` is the sum of -`f 0` plus the remaining product"] +`f 0` plus the remaining sum"] theorem prod_univ_succ [CommMonoid β] {n : ℕ} (f : Fin (n + 1) → β) : ∏ i, f i = f 0 * ∏ i : Fin n, f i.succ := prod_univ_succAbove f 0