Theorems · Theorem · combinatorics
Finset.card_union_add_card_inter
∀ {α : Type u_1} [inst : DecidableEq α] (s t : Finset α), (s ∪ t).card + (s ∩ t).card = s.card + t.card- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 66 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.induction_onproof · cited by 167
- Finset.union_emptyproof · cited by 6
- Finset.inter_emptyproof · cited by 3
Cited by14
Results whose statement or proof uses this declaration.
- Finset.dens_union_add_dens_interproof · cited by 2
- SimpleGraph.IsSRGWith.card_neighborFinset_union_eqproof · cited by 2
- Finset.card_truncatedSup_union_add_card_truncatedSup_infsproof · cited by 1
- Finset.mulETransformRight.cardproof · cited by 1
- Finset.card_union_eq_card_add_cardproof · cited by 1
- Finset.addETransformRight.cardproof · cited by 1
- Finset.pluennecke_petridis_inequality_addproof · cited by 1
- Finset.pluennecke_petridis_inequality_mulproof · cited by 1
- Finset.mulDysonETransform.cardproof · cited by 0
- Finset.cast_card_unionproof · cited by 0
- Finset.addDysonETransform.cardproof · cited by 0
- Finset.card_le_card_shattererproof · cited by 0