Theorems · Theorem · number theory

Nat.prod_pow_factorization_eq_self

∀ {f : ℕ →₀ ℕ}, (∀ p ∈ f.support, Nat.Prime p) → (f.prod fun x1 x2 => x1 ^ x2).factorization = f

Any Finsupp f : ℕ →₀ ℕ whose support is in the primes is equal to the factorization of the product ∏ (a : ℕ) ∈ f.support, a ^ f a.

Defined in

Mathlib.Data.Nat.Factorization.Defs

Cited by

4 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound