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Theorems · Theorem · order theory

Set.subset_eval_image_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {s : Set ι} {t : (i : ι) → Set (α i)},
  (s.pi t).Nonempty → ∀ (i : ι), t i ⊆ Function.eval i '' s.pi t
Defined in
Mathlib.Data.Set.Prod
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.eval_image_pi · cited by 4Set.eval_image_piFilter.map_eval_pi · cited by 2Filter.map_eval_piSet · cited by 53352SetSet.image · cited by 5609Set.imageSet.Nonempty · cited by 2627Set.Nonemptyeq_or_ne · cited by 1117eq_or_neFunction.update · cited by 502Function.updateSet.pi · cited by 405Set.piFunction.update_self · cited by 201Function.update_selfFunction.update_of_ne · cited by 198Function.update_of_neFunction.eval · cited by 140Function.evalSet.subset_eval_image_piCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.