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Theorems · Theorem · order theory

Set.eval_image_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {s : Set ι} {t : (i : ι) → Set (α i)} {i : ι},
  i ∈ s → (s.pi t).Nonempty → Function.eval i '' s.pi t = t i
Defined in
Mathlib.Data.Set.Prod
Cited by
4 results in Mathlib
Foundations
Depth 57 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.

isOpen_pi_iff · cited by 6isOpen_pi_iffSet.pi_subset_pi_iff · cited by 4Set.pi_subset_pi_iffSet.eval_image_univ_pi · cited by 4Set.eval_image_univ_piisOpenMap_eval · cited by 3isOpenMap_evalSet · cited by 53352SetSet.image · cited by 5609Set.imageSet.Nonempty · cited by 2627Set.NonemptyLE.le.antisymm · cited by 507le.antisymmSet.pi · cited by 405Set.piFunction.eval · cited by 140Function.evalSet.eval_image_pi_subset · cited by 4Set.eval_image_pi_subsetSet.subset_eval_image_pi · cited by 2Set.subset_eval_image_piSet.eval_image_piCITED BYCITES

Cites8

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Cited by4

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