Theorems · Theorem · logic and foundations
Cardinal.mk_fintype
∀ (α : Type u) [h : Fintype α], Cardinal.mk α = ↑(Fintype.card α)
- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Cardinalstatement · cited by 2,598
- Fintype.cardstatement and proof · cited by 1,386
- Cardinal.mkstatement · cited by 942
- Fintype.card_finproof · cited by 270
- Cardinal.mk_congrproof · cited by 55
- Fintype.equivOfCardEqproof · cited by 23
- Fintype.card_uliftproof · cited by 1
Cited by81
Results whose statement or proof uses this declaration.
- Module.finrank_eq_card_chooseBasisIndexproof · cited by 21
- Cardinal.lt_aleph0proof · cited by 19
- ENat.card_eq_coe_fintype_cardproof · cited by 15
- finrank_span_le_cardproof · cited by 8
- rank_eq_card_basisproof · cited by 8
- finrank_span_eq_cardproof · cited by 7
- Cardinal.mk_toNat_eq_cardproof · cited by 6
- Cardinal.mk_coe_finsetproof · cited by 5
- Module.finrank_piproof · cited by 5
- Cardinal.mk_finsupp_lift_of_fintypeproof · cited by 4
- finrank_span_set_eq_cardproof · cited by 4
- linearIndependent_le_basisproof · cited by 4