Theorems · Theorem · combinatorics
Finset.card_sdiff_of_subset
∀ {α : Type u_1} {s t : Finset α} [inst : DecidableEq α], s ⊆ t → (t \ s).card = t.card - s.card- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 2,327
- Finset.card_union_of_disjointproof · cited by 37
- Finset.sdiff_disjointproof · cited by 20
- Finset.sdiff_union_of_subsetproof · cited by 12
Cited by35
Results whose statement or proof uses this declaration.
- Nat.totient_prime_pow_succproof · cited by 4
- Finpartition.equitabilise_auxproof · cited by 3
- Finset.card_sdiffproof · cited by 3
- Finset.card_Icc_finsetproof · cited by 3
- Finset.exists_disjoint_union_of_even_cardproof · cited by 2
- IsUpperSet.card_inter_le_finsetproof · cited by 2
- SimpleGraph.card_edgeFinset_replaceVertex_of_not_adjproof · cited by 2
- Finset.mem_upShadow_iff_exists_mem_card_add_oneproof · cited by 2
- SimpleGraph.deleteFar_iffproof · cited by 2
- Finset.cast_card_sdiffproof · cited by 1
- Finset.kruskal_katona_lovasz_formproof · cited by 1
- UV.card_compressproof · cited by 1