Theorems · Theorem · logic and foundations
Set.Finite.ecard_lt_ecard
∀ {α : Type u_1} {s t : Set α}, s.Finite → s ⊂ t → ENat.card ↑s < ENat.card ↑t- Defined in
- Mathlib.SetTheory.Cardinal.NatCard
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Set.Elemstatement and proof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Set.Finitestatement and proof · cited by 1,814
- LT.lt.neproof · cited by 872
- nonpos_iff_eq_zeroproof · cited by 100
- ENat.cardstatement and proof · cited by 89
- lt_of_le_not_geproof · cited by 33
- Set.disjoint_sdiff_leftproof · cited by 25
- Set.sdiff_eq_emptyproof · cited by 24
- LT.lt.subsetproof · cited by 20
- Set.sdiff_union_of_subsetproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- Set.Finite.ecard_strictMonoOnproof · cited by 0
- Set.ecard_strictMonoproof · cited by 0