map_perm — Mathlib

English

The Set of the image map is contained in the range of f.

Русский

Множество образа map содержится в орге диапазона f.

LaTeX

$$$ (s.map f : Set \beta) \subseteq Set.range f $$$

Lean4

/-- If the only elements outside `s` are those left fixed by `σ`, then mapping by `σ` has no effect.
-/
theorem map_perm {σ : Equiv.Perm α} (hs : {a | σ a ≠ a} ⊆ s) : s.map (σ : α ↪ α) = s :=
  coe_injective <| (coe_map _ _).trans <| Set.image_perm hs

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