Theorems · Theorem · logic and foundations
Cardinal.mk_sigma
∀ {ι : Type u_2} (f : ι → Type u_1), Cardinal.mk ((i : ι) × f i) = Cardinal.sum fun i => Cardinal.mk (f i)- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equiv.symmproof · cited by 3,681
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.sumstatement · cited by 58
- Cardinal.mk_congrproof · cited by 55
- Equiv.sigmaCongrRightproof · cited by 12
- Cardinal.outMkEquivproof · cited by 6
Cited by20
Results whose statement or proof uses this declaration.
- Cardinal.mk_iUnion_le_sum_mkproof · cited by 6
- rank_piproof · cited by 6
- Cardinal.mk_list_eq_sum_powproof · cited by 5
- rank_finsuppproof · cited by 4
- Cardinal.mk_iUnion_le_sum_mk_liftproof · cited by 3
- Ordinal.lift_card_iSup_le_sum_cardproof · cited by 2
- Cardinal.sum_add_distribproof · cited by 1
- Algebra.IsAlgebraic.lift_cardinalMk_le_maxproof · cited by 1
- FirstOrder.Language.Term.card_sigmaproof · cited by 1
- Cardinal.sum_nat_eq_add_sum_succproof · cited by 1
- Cardinal.mk_le_mk_mul_of_mk_preimage_leproof · cited by 1
- FirstOrder.Language.card_emptyproof · cited by 1