Theorems · Theorem · combinatorics
Finset.notMem_singleton
∀ {α : Type u_1} {a b : α}, a ∉ {b} ↔ a ≠ b- Defined in
- Mathlib.Data.Finset.Insert
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 13,712
- Finset.mem_singletonproof · cited by 103
Cited by13
Results whose statement or proof uses this declaration.
- Finset.sum_pairproof · cited by 11
- Finset.SupIndep.pairwiseDisjointproof · cited by 7
- Finset.prod_pairproof · cited by 5
- Ring.HasFiniteQuotients.finite_cardQuot_leproof · cited by 2
- Finset.eq_zero_of_sum_eq_zeroproof · cited by 1
- Finset.centroid_pairproof · cited by 1
- Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsubproof · cited by 1
- Lagrange.interpolate_eq_add_interpolate_eraseproof · cited by 0
- Finset.card_biUnion_le_of_intersectingproof · cited by 0
- Finpartition.atomise_emptyproof · cited by 0
- Finset.eq_one_of_prod_eq_oneproof · cited by 0
- MeasureTheory.Measure.sum_restrict_leproof · cited by 0