Theorems · Theorem · order theory
Finset.union_empty
∀ {α : Type u_1} [inst : DecidableEq α] (s : Finset α), s ∪ ∅ = s- Defined in
- Mathlib.Data.Finset.Lattice.Lemmas
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 58 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.
Cites3
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
- Finset.extproof · cited by 565
- Finset.mem_unionproof · cited by 49
Cited by6
Results whose statement or proof uses this declaration.
- Finset.card_union_add_card_interproof · cited by 14
- Finset.truncatedSup_union_leftproof · cited by 2
- Finset.truncatedInf_union_leftproof · cited by 2
- exists_of_linearIndepOn_of_finite_spanproof · cited by 1
- Finset.mem_shadow_iterate_iff_exists_cardproof · cited by 1
- Nat.mul_divisors_filter_prime_powproof · cited by 1