Theorems · Theorem · logic and foundations
Cardinal.one_lt_iff_nontrivial
∀ {α : Type u}, 1 < Cardinal.mk α ↔ Nontrivial α- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement · cited by 942
- not_leproof · cited by 328
- not_nontrivial_iff_subsingletonproof · cited by 23
- Cardinal.le_one_iff_subsingletonproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- lift_rank_lt_rank_dual'proof · cited by 2
- ENat.one_lt_card_iff_nontrivialproof · cited by 1
- Cardinal.two_le_iffproof · cited by 1