closure_exchange_iff — Mathlib

English

Same as closure_exchange_iff: the exchange condition is equivalent to the stated symmetric form.

Русский

То же самое, что и closure_exchange_iff: условие обмена эквивалентно симметричной форме.

LaTeX

$$$ e \\in M.\\mathrm{closure}(\\mathrm{insert}(f,X)) \\setminus M.\\mathrm{closure}(X) \\leftrightarrow f \\in M.\\mathrm{closure}(\\mathrm{insert}(e,X)) \\setminus M.\\mathrm{closure}(X) $$$

Lean4

theorem closure_exchange_iff : e ∈ M.closure (insert f X) \ M.closure X ↔ f ∈ M.closure (insert e X) \ M.closure X :=
  ⟨closure_exchange, closure_exchange⟩

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