Theorems · Theorem · order theory
Set.image2_inter_union_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
- 4 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- le_reflproof · cited by 2,061
- le_imp_le_of_le_of_leproof · cited by 576
- Set.image2statement and proof · cited by 311
- Set.inter_commproof · cited by 291
- Set.union_selfproof · cited by 32
- Set.image2_inter_union_subset_unionproof · cited by 10
- Set.image2_commproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Set.image2_union_inter_subsetproof · cited by 3
- Finset.image₂_inter_union_subsetproof · cited by 2
- Set.inter_mul_union_subsetproof · cited by 0
- Set.inter_add_union_subsetproof · cited by 0