Theorems · Theorem · combinatorics
Finset.eq_empty_of_forall_notMem
∀ {α : Type u_1} {s : Finset α}, (∀ (x : α), x ∉ s) → s = ∅- Defined in
- Mathlib.Data.Finset.Empty
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
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.eq_of_veqproof · cited by 45
- Multiset.eq_zero_of_forall_notMemproof · cited by 13
Cited by6
Results whose statement or proof uses this declaration.
- Finset.product_emptyproof · cited by 7
- Finset.eq_empty_of_isEmptyproof · cited by 6
- Finset.singleton_inter_of_notMemproof · cited by 2
- Finset.piAntidiag_empty_of_ne_zeroproof · cited by 2
- Finset.finsuppAntidiag_empty_of_ne_zeroproof · cited by 1
- MvPolynomial.IsWeightedHomogeneous.eq_zero_of_no_monomialsproof · cited by 0