Theorems · Theorem · logic and foundations
Cardinal.sum_le_sum
∀ {ι : Type u_1} (f g : ι → Cardinal.{u_2}), (∀ (i : ι), f i ≤ g i) → Cardinal.sum f ≤ Cardinal.sum g- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.sumstatement · cited by 58
- Function.Embedding.reflproof · cited by 29
- Quot.outproof · cited by 14
- Quot.out_eqproof · cited by 9
- Function.Embedding.sigmaMapproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Cardinal.sum_le_lift_mk_mul_iSup_liftproof · cited by 4
- Cardinal.mk_list_eq_mkproof · cited by 3
- HahnSeries.cardSupp_hsum_powers_leproof · cited by 1
- Cardinal.mk_le_mk_mul_of_mk_preimage_leproof · cited by 1
- Module.Basis.le_spanproof · cited by 1
- Cardinal.mk_subtype_le_of_countable_eventually_mem_auxproof · cited by 1
- Algebra.IsAlgebraic.lift_cardinalMk_le_maxproof · cited by 1
- FirstOrder.Language.card_functions_sum_skolem₁proof · cited by 1