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Theorems · Theorem · logic and foundations

ZFSet.lift_card_iUnion_le_sum_card

∀ {α : Type u} [inst : Small.{v, u} α] {f : α → ZFSet.{v}},
  Cardinal.lift.{u, v} (ZFSet.iUnion fun i => f i).card ≤ Cardinal.sum fun i => (f i).card
Defined in
Mathlib.SetTheory.ZFC.Cardinal
Cited by
1 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Small
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ZFSet.card_vonNeumann · cited by 0ZFSet.card_vonNeumannSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalCardinal.mk · cited by 942Cardinal.mkCardinal.lift · cited by 583Cardinal.liftSmall · cited by 369SmallZFSet · cited by 259ZFSetCardinal.lift_le · cited by 78Cardinal.lift_leCardinal.sum · cited by 58Cardinal.sumCardinal.lift_umax · cited by 56Cardinal.lift_umaxCardinal.lift_lift · cited by 53Cardinal.lift_liftZFSet.card · cited by 16ZFSet.cardZFSet.iUnion · cited by 10ZFSet.iUnionZFSet.cardinalMk_coe_sort · cited by 7ZFSet.cardinalMk_coe_sortCardinal.lift_sum · cited by 5Cardinal.lift_sumCardinal.mk_iUnion_le_sum_mk_lift · cited by 3Cardinal.mk_iUnion_le_sum…ZFSet.lift_card_iUnion_le_sum…CITED BYCITES

Cites15

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Cited by1

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