Theorems · Theorem · order theory
Subtype.preimage_coe_nonempty
∀ {α : Type u_1} {s t : Set α}, (Subtype.val ⁻¹' t).Nonempty ↔ (s ∩ t).Nonempty- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Set.preimagestatement and proof · cited by 4,946
- Set.Nonemptystatement and proof · cited by 2,627
- Subtype.image_preimage_coeproof · cited by 37
- Set.image_nonemptyproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- Set.wellFoundedOn_iffproof · cited by 1