Theorems · Theorem · logic and foundations

Set.ncard_add_ncard_compl

∀ {α : Type u_1} (s : Set α),
  autoParam s.Finite Set.ncard_add_ncard_compl._auto_1 →
    autoParam sᶜ.Finite Set.ncard_add_ncard_compl._auto_3 → s.ncard + sᶜ.ncard = Nat.card α

Defined in: Mathlib.Data.Set.Card
Cited by: 16 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites10

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.univproof · cited by 3,945
Compl.complstatement and proof · cited by 2,925
Set.Finitestatement and proof · cited by 1,814
Nat.cardstatement · cited by 844
Set.ncardstatement and proof · cited by 344
Set.union_compl_selfproof · cited by 57
disjoint_compl_rightproof · cited by 47
Set.ncard_univproof · cited by 21
Set.ncard_union_eqproof · cited by 6

Cited by16

Results whose statement or proof uses this declaration.

Set.eq_univ_iff_ncardproof · cited by 4
MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
Set.even_ncard_compl_iffproof · cited by 2
Equiv.Perm.exists_mem_stabilizer_isThreeCycleproof · cited by 2
Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_cardproof · cited by 2
QuadraticForm.sigPos_weightedSumSquaresproof · cited by 2
Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_memproof · cited by 2
Function.Surjective.card_le_card_add_one_iffproof · cited by 1
alternatingGroup.exists_mem_stabilizer_smul_eqproof · cited by 1
alternatingGroup.isCoatom_stabilizerproof · cited by 1
alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1
Equiv.Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_memproof · cited by 1