Theorems · Theorem · logic and foundations
Cardinal.mk_eq_zero_iff
∀ {α : Type u}, Cardinal.mk α = 0 ↔ IsEmpty α- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, 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.
- Equivproof · cited by 8,337
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- IsEmptystatement and proof · cited by 759
- Cardinal.mk_eq_zeroproof · cited by 27
- Equiv.isEmptyproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- Cardinal.mk_ne_zero_iffproof · cited by 11
- rank_eq_zero_iffproof · cited by 3
- Subalgebra.eq_bot_of_rank_le_oneproof · cited by 3
- ENat.card_eq_zero_iff_emptyproof · cited by 3
- Subalgebra.rank_eq_one_iffproof · cited by 3
- rank_eq_one_iffproof · cited by 1
- Cardinal.zero_powerproof · cited by 1
- Cardinal.mk_embedding_eq_zero_iff_lift_ltproof · cited by 1
- Cardinal.mk_bounded_subsetproof · cited by 1
- Cardinal.mk_equiv_eq_zero_iff_lift_neproof · cited by 1
- Cardinal.mk_set_eq_zero_iffproof · cited by 1