Theorems · Theorem · logic and foundations

Set.ncard_union_eq_iff

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

Defined in: Mathlib.Data.Set.Card
Cited by: 2 results in Mathlib
Foundations: Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites9

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
Disjointstatement and proof · cited by 2,201
Set.Finitestatement and proof · cited by 1,814
Set.ncardstatement and proof · cited by 344
Set.disjoint_iff_inter_eq_emptyproof · cited by 49
Set.Finite.inter_of_leftproof · cited by 31
left_eq_addproof · cited by 15
Set.ncard_eq_zeroproof · cited by 7
Set.ncard_union_add_ncard_interproof · cited by 4

Cited by2

Results whose statement or proof uses this declaration.

Set.ncard_union_ltproof · cited by 1
Set.ncard_sumEquiv_symm_applyproof · cited by 1