Theorems · Theorem · combinatorics
Fin.exists_ne_and_ne_of_two_lt
∀ {n : ℕ} (i j : Fin n), 2 < n → ∃ k, k ≠ i ∧ k ≠ jIf working with more than two elements, we can always pick a third distinct from two existing elements.
- Defined in
- Mathlib.Data.Fin.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by4
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.touchpoint_injectiveproof · cited by 4
- Affine.Simplex.excenter_singleton_injectiveproof · cited by 2
- Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mulproof · cited by 2
- Affine.Simplex.ExcenterExists.touchpoint_ne_pointproof · cited by 1