compress_self — Mathlib

English

If insert a s belongs to the down-compressed family, then s also belongs to it.

Русский

Если insert a s принадлежит down-компрессии, то и сам s принадлежит ей.

LaTeX

$$$\\text{mem\\_compression\\_of\\_insert\\_mem\\_compression}: \\text{If } (\\mathrm{insert}\\ a\\ s) \\in 𝓓(a,\\mathcal{A}) \\text{ then } s \\in 𝓓(a,\\mathcal{A}).$$$

Lean4

@[simp]
theorem compress_self (u a : α) : compress u u a = a :=
  by
  unfold compress
  split_ifs with h
  · exact h.1.symm.sup_sdiff_cancel_right
  · rfl

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