Theorems · Theorem · order theory
SetLike.exists
∀ {A : Type u_1} {B : Type u_2} [i : SetLike A B] {p : A} {q : ↥p → Prop}, (∃ x, q x) ↔ ∃ x, ∃ (h : x ∈ p), q ⟨x, h⟩- Defined in
- Mathlib.Data.SetLike.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- SetLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLikestatement and proof · cited by 1,084
- SetCoe.existsproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- QuotientAddGroup.preimage_image_mkproof · cited by 2
- AddMonoidHom.domRestrict_rangeproof · cited by 1
- AddSubgroup.mem_sup'proof · cited by 0