Theorems · Theorem · logic and foundations
Equiv.Set.sumCompl_symm_apply_of_mem
∀ {α : Type u} {s : Set α} [inst : DecidablePred fun x => x ∈ s] {x : α} (hx : x ∈ s),
(Equiv.Set.sumCompl s).symm x = Sum.inl ⟨x, hx⟩- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Quot.sound
- Assumes
- DecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Equiv.symmstatement · cited by 3,681
- Compl.complstatement · cited by 2,925
- Equiv.Set.sumComplstatement · cited by 16
- Equiv.sumCompl_symm_apply_of_posproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.extend_functionproof · cited by 2