Theorems · Definition · logic and foundations
Equiv.Set.sumDiffSubset
{α : Type u_3} → {s t : Set α} → s ⊆ t → [DecidablePred fun x => x ∈ s] → ↑s ⊕ ↑(t \ s) ≃ ↑tsumDiffSubset s t is the natural equivalence between
s ⊕ (t \ s) and t, where s and t are two sets.
- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 59 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.
Cites6
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
- Equiv.symmproof · cited by 3,681
- Equiv.setCongrproof · cited by 13
- Equiv.Set.unionproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- Equiv.Set.sumDiffSubset.congr_simpstatement and proof · cited by 0
- Equiv.Set.sumDiffSubset_apply_inlstatement · cited by 0
- Equiv.Set.sumDiffSubset_apply_inrstatement · cited by 0
- Equiv.Set.sumDiffSubset_symm_apply_of_memstatement and proof · cited by 0
- Equiv.Set.sumDiffSubset_symm_apply_of_notMemstatement and proof · cited by 0
- Module.Basis.sumExtendproof · cited by 0