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Theorems · Theorem · order theory

Set.univ_pi_eq_singleton_iff

∀ {ι : Type u_1} {α : ι → Type u_2} {t : (i : ι) → Set (α i)} {a : (i : ι) → α i},
  Set.univ.pi t = {a} ↔ ∀ (i : ι), t i = {a i}
Defined in
Mathlib.Data.Set.Prod
Cited by
4 results in Mathlib
Foundations
Depth 24 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.

AddSubgroup.pi_eq_bot_iff · cited by 2AddSubgroup.pi_eq_bot_iffSubgroup.pi_eq_bot_iff · cited by 1Subgroup.pi_eq_bot_iffAddSubmonoid.pi_eq_bot_iff · cited by 0AddSubmonoid.pi_eq_bot_iffSubmonoid.pi_eq_bot_iff · cited by 0Submonoid.pi_eq_bot_iffSet · cited by 53352SetSet.univ · cited by 3945Set.univFunction.update · cited by 502Function.updateSet.pi · cited by 405Set.piFunction.update_self · cited by 201Function.update_selfSet.update_mem_pi_iff_of_mem · cited by 5Set.update_mem_pi_iff_of_…Set.univ_pi_eq_singleton_iffCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.