restrictSubtype — Mathlib

English

Given M on α and X ⊆ α, the restriction of M to X is the matroid on X with ground set univ, always isomorphic to M ↾ X.

Русский

Дано M на α и X ⊆ α, ограничение M к X — матроид на X сground set равным единице, всегда изоморален M ↾ X.

LaTeX

$$$\text{restrictSubtype}(M,X) = (M \restriction X).comap(↑)$$$

Lean4

/-- Given `M : Matroid α` and `X : Set α`, the restriction of `M` to `X`,
viewed as a matroid on type `X` with ground set `univ`.
Always isomorphic to `M ↾ X`. If `X = M.E`, then isomorphic to `M`. -/
def restrictSubtype (M : Matroid α) (X : Set α) : Matroid X :=
  (M ↾ X).comap (↑)

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