attachFin_ssubset_attachFin_iff — Mathlib

English

For hs ht, the strict subset relation between s.attachFin hs and t.attachFin ht is equivalent to the strict subset relation between s and t.

Русский

Для несоблюдения строгого подмножества между s.attachFin и t.attachFin верно эквивалентно строгому подмножеству между s и t.

LaTeX

$$s.attachFin hs ⊂ t.attachFin ht \\Leftrightarrow s ⊂ t$$

Lean4

@[simp]
theorem attachFin_ssubset_attachFin_iff {s t : Finset ℕ} (hs : ∀ m ∈ s, m < n) (ht : ∀ m ∈ t, m < n) :
    s.attachFin hs ⊂ t.attachFin ht ↔ s ⊂ t := by simp [← map_ssubset_map (f := Fin.valEmbedding)]

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