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Theorems · Theorem · order theory

Set.pi_congr

∀ {ι : Type u_1} {α : ι → Type u_2} {s₁ s₂ : Set ι} {t₁ t₂ : (i : ι) → Set (α i)},
  s₁ = s₂ → (∀ i ∈ s₁, t₁ i = t₂ i) → s₁.pi t₁ = s₂.pi t₂
Defined in
Mathlib.Data.Set.Prod
Cited by
4 results in Mathlib
Foundations
Depth 16 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.

MeasureTheory.isPiSystem_squareCylinders · cited by 3MeasureTheory.isPiSystem_…dense_pi · cited by 2dense_piSet.pi_update_of_notMem · cited by 1Set.pi_update_of_notMemBoxIntegral.Box.iUnion_Ioo_of_tendsto · cited by 0Box.iUnion_Ioo_of_tendstoSet · cited by 53352SetSet.pi · cited by 405Set.piSet.pi_congrCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Setstatement and proof · cited by 53,352
  • Set.pistatement · cited by 405

Cited by4

Results whose statement or proof uses this declaration.