Theorems · Theorem · order theory
Set.image2_eq_empty_iff
∀ {α : Type u_1} {β : Type u_3} {γ : Type u_5} {f : α → β → γ} {s : Set α} {t : Set β},
Set.image2 f s t = ∅ ↔ s = ∅ ∨ t = ∅- Defined in
- Mathlib.Data.Set.NAry
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- not_and_orproof · cited by 82
- Set.not_nonempty_iff_eq_emptyproof · cited by 56
- Set.image2_nonempty_iffproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- Set.sups_eq_emptyproof · cited by 0
- Set.sdiv_eq_emptyproof · cited by 0
- Set.infs_eq_emptyproof · cited by 0
- Set.sub_eq_emptyproof · cited by 0
- Set.vadd_eq_emptyproof · cited by 0
- Set.vsub_eq_emptyproof · cited by 0
- Set.div_eq_emptyproof · cited by 0
- Set.add_eq_emptyproof · cited by 0
- Set.mul_eq_emptyproof · cited by 0
- Set.smul_eq_emptyproof · cited by 0