Theorems · Theorem · logic and foundations
Cardinal.mk_eq_zero
∀ (α : Type u) [IsEmpty α], Cardinal.mk α = 0
- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses Quot.sound
- Assumes
- IsEmpty
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
- IsEmptystatement and proof · cited by 759
- Equiv.cardinal_eqproof · cited by 35
- Equiv.equivOfIsEmptyproof · cited by 4
Cited by27
Results whose statement or proof uses this declaration.
- rank_subsingleton'proof · cited by 13
- Cardinal.mk_eq_zero_iffproof · cited by 11
- Cardinal.lift_zeroproof · cited by 11
- Nat.card_of_isEmptyproof · cited by 6
- Ordinal.card_zeroproof · cited by 4
- Order.cof_eq_zero_iffproof · cited by 3
- MvPolynomial.cardinalMk_le_max_liftproof · cited by 2
- ZFSet.card_emptyproof · cited by 2
- FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_leproof · cited by 2
- WType.cardinalMk_le_max_aleph0_of_finite'proof · cited by 2
- HahnSeries.cardSupp_zeroproof · cited by 2
- Submodule.spanRank_eq_zero_iff_eq_botproof · cited by 1