Theorems · Theorem · order theory
Set.image2_union_inter_subset
∀ {α : Type u_1} {β : Type u_3} {f : α → α → β} {s t : Set α},
(∀ (a b : α), f a b = f b a) → Set.image2 f (s ∪ t) (s ∩ t) ⊆ Set.image2 f s t- Defined in
- Mathlib.Data.Set.NAry
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 311
- Set.image2_commproof · cited by 4
- Set.image2_inter_union_subsetproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Finset.image₂_union_inter_subsetproof · cited by 2
- Set.union_mul_inter_subsetproof · cited by 0
- Set.union_add_inter_subsetproof · cited by 0