source_inter_preimage_eq — Mathlib

English

Preimages are respected by equivalence: e.source ∩ e^{-1}(s) = e'.source ∩ e'^{-1}(s) when e ≈ e'.

Русский

Оба предобраза уравновешиваются эквивалентностью: e.source ∩ e^{-1}(s) = e'.source ∩ e'^{-1}(s) при e ≈ e'.

LaTeX

$$$ e.source \\cap e^{-1}(s) = e'.source \\cap e'^{-1}(s) $$$

Lean4

/-- Preimages are respected by equivalence. -/
theorem source_inter_preimage_eq {e e' : PartialEquiv α β} (he : e ≈ e') (s : Set β) :
    e.source ∩ e ⁻¹' s = e'.source ∩ e' ⁻¹' s := by rw [he.eqOn.inter_preimage_eq, source_eq he]

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