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.
- Set.add_mem_addproof · cited by 30
- Set.image2_subsetproof · cited by 25
- Set.mul_mem_mulproof · cited by 22
- Set.Nonempty.image2proof · cited by 14
- ContinuousMap.isOpen_setOfPred_mapsToproof · cited by 9
- Set.smul_mem_smulproof · cited by 9
- Set.image2_iInter₂_subset_leftproof · cited by 8
- Set.image2_iInter₂_subset_rightproof · cited by 8
- Set.image_subset_image2_rightproof · cited by 8
- Set.image2_iInter_subset_leftproof · cited by 7
- Set.image2_iInter_subset_rightproof · cited by 7
- Set.image_subset_image2_leftproof · cited by 5