Theorems · Theorem · combinatorics
Finset.eq_empty_of_isEmpty
∀ {α : Type u_1} [IsEmpty α] (s : Finset α), s = ∅A Finset for an empty type is empty.
- Defined in
- Mathlib.Data.Finset.Empty
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- IsEmptystatement and proof · cited by 759
- isEmptyElimproof · cited by 59
- Finset.eq_empty_of_forall_notMemproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Finset.sum_of_isEmptyproof · cited by 3
- Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_invproof · cited by 2
- weightedVSub_mem_vectorSpanproof · cited by 2
- Finset.univ_finset_of_isEmptyproof · cited by 1
- Finset.prod_of_isEmptyproof · cited by 1
- Finset.dens_eq_zeroproof · cited by 1