Theorems · Theorem · order theory
Set.SurjOn.union_union
∀ {α : Type u_1} {β : Type u_2} {s₁ s₂ : Set α} {t₁ t₂ : Set β} {f : α → β},
Set.SurjOn f s₁ t₁ → Set.SurjOn f s₂ t₂ → Set.SurjOn f (s₁ ∪ s₂) (t₁ ∪ t₂)- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.SurjOnstatement and proof · cited by 186
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
- Set.Subset.reflproof · cited by 66
- Set.SurjOn.monoproof · cited by 13
- Set.SurjOn.unionproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Set.BijOn.unionproof · cited by 1
- surjOn_Ici_of_monotone_surjectiveproof · cited by 1