Theorems · Theorem · logic and foundations
Cardinal.sum_lt_prod
- 1000+ list: König's theorem (set theory)
∀ {ι : Type u_1} (f g : ι → Cardinal.{u_2}), (∀ (i : ι), f i < g i) → Cardinal.sum f < Cardinal.prod gKönig's theorem
- Defined in
- Mathlib.SetTheory.Cardinal.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Cardinalstatement and proof · cited by 2,598
- Function.Embeddingproof · cited by 988
- Cardinal.mkproof · cited by 942
- lt_of_not_geproof · cited by 374
- LT.lt.not_geproof · cited by 305
- Quotient.outproof · cited by 141
- Function.invFunproof · cited by 60
- Cardinal.sumstatement and proof · cited by 58
- Function.Embedding.inj'proof · cited by 29
- LT.lt.ne_botproof · cited by 26
- Cardinal.prodstatement and proof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.lt_power_cof_ordproof · cited by 2