Theorems · Theorem · logic and foundations
Cardinal.exists_notMem_of_length_lt
∀ {α : Type u_1} (l : List α), ↑l.length < Cardinal.mk α → ∃ z, z ∉ l- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.univproof · cited by 3,945
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Nat.cast_leproof · cited by 159
- Cardinal.mk_le_mk_of_subsetproof · cited by 37
- List.mem_toFinsetproof · cited by 20
- Cardinal.mk_univproof · cited by 12
- Cardinal.mk_coe_finsetproof · cited by 5
- List.toFinset_card_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.exists_ne_ne_of_three_leproof · cited by 4