Theorems · Definition · logic and foundations
Equiv.Set.union
{α : Type u_3} → {s t : Set α} → [DecidablePred fun x => x ∈ s] → Disjoint s t → ↑(s ∪ t) ≃ ↑s ⊕ ↑tIf sets s and t are disjoint, then s ∪ t is equivalent to s ⊕ t.
- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Disjointstatement and proof · cited by 2,201
- Equiv.Set.union'proof · cited by 0
Cited by16
Results whose statement or proof uses this declaration.
- Set.encard_union_eqproof · cited by 15
- Equiv.Finset.unionproof · cited by 9
- Equiv.Set.insertproof · cited by 6
- LinearIndepOn.unionproof · cited by 5
- Equiv.Set.sumDiffSubsetproof · cited by 5
- Equiv.Finset.disjUnionEquivproof · cited by 5
- Cardinal.mk_union_of_disjointproof · cited by 4
- Equiv.toComplproof · cited by 4
- Equiv.Set.union_apply_leftstatement · cited by 2
- Equiv.Set.union_apply_rightstatement · cited by 2
- Set.Finite.ecard_lt_ecardproof · cited by 2
- Equiv.Set.unionSumInterproof · cited by 1