Theorems · Theorem · logic and foundations

Set.ncard_union_eq

∀ {α : Type u_1} {s t : Set α},
  Disjoint s t →
    autoParam s.Finite Set.ncard_union_eq._auto_1 →
      autoParam t.Finite Set.ncard_union_eq._auto_3 → (s ∪ t).ncard = s.ncard + t.ncard

Defined in: Mathlib.Data.Set.Card
Cited by: 6 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites11

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
ENatproof · cited by 4,985
Disjointstatement and proof · cited by 2,201
Set.Finitestatement and proof · cited by 1,814
Nat.cast_addproof · cited by 586
Set.ncardstatement and proof · cited by 344
Set.encardproof · cited by 327
Set.Finite.unionproof · cited by 74
Nat.cast_injproof · cited by 70
Set.Finite.cast_ncard_eqproof · cited by 28
Set.encard_union_eqproof · cited by 15

Cited by6

Results whose statement or proof uses this declaration.

Set.ncard_add_ncard_complproof · cited by 16
Set.ncard_inter_add_ncard_sdiff_eq_ncardproof · cited by 4
Set.ncard_sdiff_add_ncardproof · cited by 1
NumberField.InfinitePlace.unramifedPlacesOver_ncard_add_eq_finrankproof · cited by 1
Set.exists_union_disjoint_cardinal_eq_iffproof · cited by 0
Set.Infinite.exists_superset_ncard_eqproof · cited by 0