Theorems · Theorem · logic and foundations
Cardinal.exists_ne_ne_of_three_le
∀ {α : Type u_1}, 3 ≤ Cardinal.mk α → ∀ (x y : α), ∃ z, z ≠ x ∧ z ≠ y- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Nat.cast_add_oneproof · cited by 56
- Cardinal.natCast_add_one_le_iffproof · cited by 5
- Cardinal.exists_notMem_of_length_ltproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Monoid.CoprodI.lift_word_prod_nontrivial_of_head_cardproof · cited by 1
- Monoid.CoprodI.lift_word_prod_nontrivial_of_not_emptyproof · cited by 1
- ENat.exists_ne_ne_of_three_leproof · cited by 0
- Cardinal.three_leproof · cited by 0