Theorems · Theorem · logic and foundations
Cardinal.lift_sum
∀ {ι : Type u} (f : ι → Cardinal.{v}),
Cardinal.lift.{w, max v u} (Cardinal.sum f) = Cardinal.sum fun i => Cardinal.lift.{w, v} (f i)- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkproof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Nonempty.someproof · cited by 340
- Equiv.transproof · cited by 337
- Quotient.outproof · cited by 141
- Equiv.uliftproof · cited by 115
- Cardinal.sumstatement · cited by 58
- Cardinal.lift_liftproof · cited by 53
- Equiv.cardinal_eqproof · cited by 35
- Cardinal.mk_outproof · cited by 14
- Equiv.sigmaCongrRightproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.sum_le_lift_mk_mul_iSup_liftproof · cited by 4
- Cardinal.mk_iUnion_le_liftproof · cited by 2
- FirstOrder.Language.card_eq_card_functions_add_card_relationsproof · cited by 1
- ZFSet.lift_card_iUnion_le_sum_cardproof · cited by 1
- FirstOrder.Language.card_sumproof · cited by 1