Theorems · Theorem · logic and foundations
Set.sdiff_nonempty_of_ncard_lt_ncard
∀ {α : Type u_1} {s t : Set α},
s.ncard < t.ncard → autoParam s.Finite Set.sdiff_nonempty_of_ncard_lt_ncard._auto_1 → (t \ s).Nonempty- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Nonemptystatement · cited by 2,627
- Set.Finitestatement and proof · cited by 1,814
- Set.ncardstatement and proof · cited by 344
- LT.lt.not_geproof · cited by 305
- Set.nonempty_iff_ne_emptyproof · cited by 96
- Set.sdiff_eq_emptyproof · cited by 24
- Set.ncard_le_ncardproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- alternatingGroup.exists_mem_stabilizer_smul_eqproof · cited by 1
- Set.diff_nonempty_of_ncard_lt_ncardproof · cited by 0
- Set.exists_mem_notMem_of_ncard_lt_ncardproof · cited by 0