English
Under the same hypothesis as Set:Sized, assorted simplified equalities about membership under uv-compression hold and reduce to standard equalities.
Русский
При тех же условиях, что Set.Sized, выполняются упрощенные леммы принадлежности и равенства под сжатием uv.
LaTeX
$$Set.Sized uvCompression simp lemmas for membership$$
Lean4
theorem _root_.Set.Sized.uvCompression (huv : #u = #v) (h𝒜 : (𝒜 : Set (Finset α)).Sized r) :
(𝓒 u v 𝒜 : Set (Finset α)).Sized r :=
by
simp_rw [Set.Sized, mem_coe, mem_compression]
rintro s (hs | ⟨huvt, t, ht, rfl⟩)
· exact h𝒜 hs.1
· rw [card_compress huv, h𝒜 ht]