image_prodMap — Mathlib

English

If U is symmetric, then the image of U under Prod.map f f is symmetric.

Русский

Если U симметрично, то образ Under Prod.map f f симметричен.

LaTeX

$$IsSymmetricRel U → IsSymmetricRel (Set.image (Prod.map f f) U)$$

Lean4

theorem image_prodMap {U : Set (α × α)} (ht : IsSymmetricRel U) (f : α → β) : IsSymmetricRel (Prod.map f f '' U) := by
  rw [IsSymmetricRel, ← image_swap_eq_preimage_swap, ← image_comp, ← Prod.map_comp_swap, image_comp,
    image_swap_eq_preimage_swap, ht]

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