restrict_loops_eq' — Mathlib

English

A version of restrict_loops_eq without the hypothesis R ⊆ M.E.

Русский

Версия равенстваRestriction петель без предположения R ⊆ M.E.

LaTeX

$$$ (M \restriction R).loops = (M.loops \cap R) \cup (R \setminus M.E) $$$

Lean4

/-- A version of `restrict_loops_eq` without the hypothesis that `R ⊆ M.E` -/
theorem restrict_loops_eq' (M : Matroid α) (R : Set α) : (M ↾ R).loops = (M.loops ∩ R) ∪ (R \ M.E) := by
  rw [← closure_empty, ← closure_empty, restrict_closure_eq', empty_inter]

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