Theorems · Definition · logic and foundations
Cardinal.prod
{ι : Type u} → (ι → Cardinal.{u_1}) → Cardinal.{max u u_1}The indexed product of cardinals is the cardinality of the Pi type (dependent product).
- Defined in
- Mathlib.SetTheory.Cardinal.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Quotient.outproof · cited by 141
Cited by16
Results whose statement or proof uses this declaration.
- Cardinal.mk_pistatement · cited by 11
- Cardinal.prod_conststatement · cited by 8
- Cardinal.mk_setproof · cited by 3
- Cardinal.prod_const'statement · cited by 3
- Cardinal.lift_prodstatement · cited by 2
- Cardinal.mk_perm_eq_self_powerproof · cited by 2
- Field.Emb.cardinal_eq_two_pow_rankproof · cited by 2
- Cardinal.prod_eq_of_fintypestatement and proof · cited by 2
- Cardinal.prod_le_prodstatement · cited by 2
- Cardinal.lift_power_sumstatement · cited by 1
- Cardinal.sum_lt_prodstatement and proof · cited by 1
- continuum_le_cardinal_of_nontriviallyNormedFieldproof · cited by 1