Theorems · Theorem · logic and foundations
Cardinal.mk_ne_zero_iff
∀ {α : Type u}, Cardinal.mk α ≠ 0 ↔ Nonempty α- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 25 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 · cited by 2,598
- Cardinal.mkstatement · cited by 942
- not_iff_notproof · cited by 159
- not_isEmpty_iffproof · cited by 19
- Cardinal.mk_eq_zero_iffproof · cited by 11
Cited by11
Results whose statement or proof uses this declaration.
- Cardinal.power_le_power_leftproof · cited by 9
- Cardinal.eq_one_iff_uniqueproof · cited by 3
- Cardinal.mk_ne_zeroproof · cited by 2
- Cardinal.power_ne_zeroproof · cited by 2
- Cardinal.mk_set_ne_zero_iffproof · cited by 1
- Cardinal.sum_lt_prodproof · cited by 1
- FirstOrder.Language.Term.card_sigmaproof · cited by 1
- Cardinal.zero_powerproof · cited by 1
- FirstOrder.Language.exists_elementarySubstructure_card_eqproof · cited by 1
- Cardinal.nonempty_outproof · cited by 1
- Field.Emb.Cardinal.eq_bot_of_not_nonemptyproof · cited by 0