factoredNumbers_empty — Mathlib

English

The set of factored numbers for the empty set equals {1}.

Русский

Множество фактoredNumbers для пустого множества равно {1}.

LaTeX

$$factoredNumbers(\emptyset) = \{1\}$$

Lean4

@[simp]
theorem factoredNumbers_empty : factoredNumbers ∅ = { 1 } :=
  by
  ext m
  simp only [mem_factoredNumbers, Finset.notMem_empty, ← List.eq_nil_iff_forall_not_mem, primeFactorsList_eq_nil,
    and_or_left, not_and_self_iff, ne_and_eq_iff_right zero_ne_one, false_or, Set.mem_singleton_iff]

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