Theorems · Theorem · combinatorics
Finset.card_le_card
∀ {α : Type u_1} {s t : Finset α}, s ⊆ t → s.card ≤ t.card- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 56 from the axioms, rests on 899 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Finset.cardstatement · cited by 2,327
- Finset.val_le_iffproof · cited by 11
- Multiset.card_le_cardproof · cited by 11
Cited by118
Results whose statement or proof uses this declaration.
- Finset.card_le_univproof · cited by 32
- Finset.card_monoproof · cited by 24
- Finset.card_filter_leproof · cited by 16
- Finset.card_le_card_of_injOnproof · cited by 16
- ThreeAPFree.le_addRothNumberproof · cited by 7
- Finset.all_card_le_biUnion_card_iff_exists_injectiveproof · cited by 6
- ThreeGPFree.le_mulRothNumberproof · cited by 6
- ZLattice.rankproof · cited by 5
- partialSups_disjointedproof · cited by 5
- Fin.lt_card_filter_univ_iff_apply_of_impproof · cited by 4
- Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceproof · cited by 4
- Finpartition.equitabilise_auxproof · cited by 3