Theorems · Theorem · combinatorics
Finset.Nonempty.ne_empty
∀ {α : Type u_1} {s : Finset α}, s.Nonempty → s ≠ ∅- Defined in
- Mathlib.Data.Finset.Empty
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 58 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.Nonemptystatement and proof · cited by 1,001
- Finset.ne_empty_of_memproof · cited by 3
Cited by22
Results whose statement or proof uses this declaration.
- Finset.nonempty_iff_ne_emptyproof · cited by 34
- Finset.singleton_ne_emptyproof · cited by 6
- Finset.le_sum_nonempty_of_subadditive_on_predproof · cited by 3
- Finpartition.equitabilise_auxproof · cited by 3
- Finset.pluennecke_ruzsa_inequality_pow_div_pow_mulproof · cited by 2
- Finset.le_prod_nonempty_of_submultiplicative_on_predproof · cited by 2
- Finset.Nonempty.subset_singleton_iffproof · cited by 2
- Finset.ruzsa_triangle_inequality_add_add_addproof · cited by 2
- Finset.ruzsa_triangle_inequality_mul_mul_mulproof · cited by 2
- Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_addproof · cited by 2
- Finpartition.exists_equipartition_card_eqproof · cited by 1
- Finpartition.IsEquipartition.sum_nonUniforms_lt'proof · cited by 1