Theorems · Theorem · logic and foundations

Set.ncard_compl

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

Defined in: Mathlib.Data.Set.Card
Cited by: 1 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites6

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
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.ncard_add_ncard_complproof · cited by 16

Cited by1

Results whose statement or proof uses this declaration.

Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomialproof · cited by 1