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Theorems · Theorem · logic and foundations

Set.mem_image2_of_mem

∀ {α : Type u} {β : Type v} {γ : Type w} {f : α → β → γ} {s : Set α} {t : Set β} {a : α} {b : β},
  a ∈ s → b ∈ t → f a b ∈ Set.image2 f s t
Defined in
Mathlib.Data.Set.Operations
Cited by
40 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms

Around this declaration

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

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.image2statement · cited by 311

Cited by40

Results whose statement or proof uses this declaration.