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Theorems · Theorem · order theory

Set.diagonal_subset_iff

∀ {α : Type u_1} {s : Set (α × α)}, Set.diagonal α ⊆ s ↔ ∀ (x : α), (x, x) ∈ s
Defined in
Mathlib.Data.Set.Prod
Cited by
1 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.

Set.mapsTo_prodMap_diagonal · cited by 1Set.mapsTo_prodMap_diagon…Set · cited by 53352SetSet.diagonal · cited by 42Set.diagonalSet.diagonal_subset_iffCITED 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.diagonalstatement · cited by 42

Cited by1

Results whose statement or proof uses this declaration.