Theorems · Theorem · order theory
Finset.mem_union
∀ {α : Type u_1} [inst : DecidableEq α] {s t : Finset α} {a : α}, a ∈ s ∪ t ↔ a ∈ s ∨ a ∈ t- Defined in
- Mathlib.Data.Finset.Lattice.Basic
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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.
- Finsetstatement and proof · cited by 13,712
- Multiset.mem_ndunionproof · cited by 3
Cited by49
Results whose statement or proof uses this declaration.
- Finset.coe_unionproof · cited by 78
- Finset.mem_union_leftproof · cited by 15
- Finset.mem_union_rightproof · cited by 15
- HasSum.nat_add_negproof · cited by 10
- ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetproof · cited by 8
- Finset.empty_unionproof · cited by 8
- Finset.union_emptyproof · cited by 6
- Equiv.Perm.support_mul_leproof · cited by 6
- HasSum.nat_add_neg_add_oneproof · cited by 5
- ProbabilityTheory.Kernel.indepSets_piiUnionInter_of_disjointproof · cited by 4
- Equiv.Perm.Disjoint.support_mulproof · cited by 4
- Finset.notMem_unionproof · cited by 3