Theorems · Theorem · logic and foundations
Cardinal.lift_natCast
∀ (n : ℕ), Cardinal.lift.{u, v} ↑n = ↑n- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Cardinalstatement · cited by 2,598
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Nat.cast_addproof · cited by 586
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.lift_oneproof · cited by 33
- Cardinal.lift_addproof · cited by 18
- Cardinal.lift_zeroproof · cited by 11
Cited by39
Results whose statement or proof uses this declaration.
- Cardinal.lt_aleph0proof · cited by 19
- Cardinal.lift_ofENatproof · cited by 7
- Cardinal.lift_ofNatproof · cited by 7
- finrank_span_eq_cardproof · cited by 7
- Module.finrank_piproof · cited by 5
- Cardinal.mk_finsupp_lift_of_fintypeproof · cited by 4
- Module.Basis.card_le_card_of_linearIndependentproof · cited by 3
- LinearIndependent.lt_aleph0_of_finiteproof · cited by 3
- Cardinal.nat_lt_lift_iffproof · cited by 3
- rank_fun_eq_lift_mulproof · cited by 2
- LinearIndependent.cardinalMk_le_finrankproof · cited by 2
- exists_linearIndependent_cons_of_lt_rankproof · cited by 2