Theorems · Theorem · logic and foundations
Set.Finite.encard_lt_encard
∀ {α : Type u_1} {s t : Set α}, s.Finite → s ⊂ t → s.encard < t.encard- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENatstatement · cited by 4,985
- Set.Finitestatement and proof · cited by 1,814
- LT.lt.neproof · cited by 872
- Eq.leproof · cited by 605
- Set.encardstatement and proof · cited by 327
- LE.le.lt_of_neproof · cited by 116
- LT.lt.subsetproof · cited by 20
- Set.encard_monoproof · cited by 8
- Set.Finite.eq_of_subset_of_encard_leproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- Set.ncard_lt_ncardproof · cited by 5
- Set.Finite.encard_strictMonoOnproof · cited by 0
- Set.encard_strictMonoproof · cited by 0
- Set.Finite.encard_lt_cardproof · cited by 0