Theorems · Theorem · logic and foundations

Set.ncard_union_lt

∀ {α : Type u_1} {s t : Set α},
  autoParam s.Finite Set.ncard_union_lt._auto_1 →
    autoParam t.Finite Set.ncard_union_lt._auto_3 → ¬Disjoint s t → (s ∪ t).ncard < s.ncard + t.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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Cites7

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 · cited by 344
LE.le.lt_of_neproof · cited by 116
Set.ncard_union_leproof · cited by 4
Set.ncard_union_eq_iffproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_interproof · cited by 1