eq_replicate — Mathlib

English

s = replicate n a iff card(s) = n and ∀ b ∈ s, b = a.

Русский

s = replicate n a тогда и только тогда, когда card(s) = n и ∀ b ∈ s, b = a.

LaTeX

$$$s = \\operatorname{replicate}(n,a) \\iff \\operatorname{card}(s) = n \\land \\forall b \\in s, b = a$$$

Lean4

theorem eq_replicate {a : α} {n} {s : Multiset α} : s = replicate n a ↔ card s = n ∧ ∀ b ∈ s, b = a :=
  ⟨fun h => h.symm ▸ ⟨card_replicate _ _, fun _b => eq_of_mem_replicate⟩, fun ⟨e, al⟩ => e ▸ eq_replicate_of_mem al⟩

Похожие утверждения