Theorems · Theorem · logic and foundations

Set.ncard_union_add_ncard_inter

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

Defined in: Mathlib.Data.Set.Card
Cited by: 4 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites12

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
Set.Finitestatement and proof · cited by 1,814
Nat.cast_addproof · cited by 586
Set.inter_subset_leftproof · cited by 360
Set.ncardstatement and proof · cited by 344
Set.encardproof · cited by 327
Set.Finite.subsetproof · cited by 285
Set.Finite.unionproof · cited by 74
Nat.cast_injproof · cited by 70
Set.Finite.cast_ncard_eqproof · cited by 28
Set.encard_union_add_encard_interproof · cited by 3

Cited by4

Results whose statement or proof uses this declaration.

Set.ncard_union_eq_iffproof · cited by 2
Set.nonempty_inter_of_le_ncard_add_ncardproof · cited by 1
Set.ncard_inter_add_ncard_unionproof · cited by 0
Set.nonempty_inter_of_lt_ncard_add_ncardproof · cited by 0