Theorems · Theorem · logic and foundations
Set.mem_prod
∀ {α : Type u} {β : Type v} {s : Set α} {t : Set β} {p : α × β}, p ∈ s ×ˢ t ↔ p.1 ∈ s ∧ p.2 ∈ t- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 6 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
- SProd.sprodstatement · cited by 1,750
Cited by32
Results whose statement or proof uses this declaration.
- Set.mapsTo_snd_prodproof · cited by 9
- Set.mapsTo_fst_prodproof · cited by 8
- biInf_prodproof · cited by 4
- Set.addCenter_prodproof · cited by 3
- Set.prod_vsub_prod_commproof · cited by 2
- Finset.le_addEnergyproof · cited by 2
- ProperVAdd.isCompact_setOfPred_inter_nonemptyproof · cited by 2
- MeasureTheory.measurable_measure_add_rightproof · cited by 2
- IsGLB.prodproof · cited by 1
- IsTopologicalAddGroup.exists_antitone_basis_nhds_zeroproof · cited by 1
- Set.PairwiseDisjoint.prod_leftproof · cited by 1
- FDerivMeasurableAux.isOpen_A_with_paramproof · cited by 1