Theorems · Theorem · logic and foundations
Cardinal.eq
∀ {α β : Type u}, Cardinal.mk α = Cardinal.mk β ↔ Nonempty (α ≃ β)- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Quotient.eq'proof · cited by 14
Cited by17
Results whose statement or proof uses this declaration.
- Cardinal.mk_sigma_congrproof · cited by 1
- Set.Infinite.exists_union_disjoint_cardinal_eq_of_infiniteproof · cited by 1
- Cardinal.mk_pi_congrproof · cited by 1
- Infinite.nonempty_fieldproof · cited by 1
- Cardinal.mk_pi_congr_propproof · cited by 1
- Cardinal.mk_preimage_downproof · cited by 1
- FirstOrder.Field.ACF_categoricalproof · cited by 1
- Cardinal.mk_embedding_eq_arrow_of_lift_leproof · cited by 1
- SimpleGraph.IsClique.even_iff_exists_isMatchingproof · cited by 1
- ModuleCat.free_shortExact_rank_addproof · cited by 1
- Cardinal.mk_sigma_congr'proof · cited by 0
- CategoryTheory.HomOrthogonal.equiv_of_isoproof · cited by 0