Theorems · Theorem · logic and foundations
Set.sep_eq_inter_sep
∀ {α : Type u_1} {s t : Set α} {p : α → Prop}, s ⊆ t → {x | x ∈ s ∧ p x} = s ∩ {x | x ∈ t ∧ p x}- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, 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.ofPredstatement and proof · cited by 6,101
- Set.inter_assocproof · cited by 67
- Set.left_eq_interproof · cited by 4
- Set.inter_ofPred_eq_sepproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Convex.quasiconvexOn_restrictproof · cited by 1
- Convex.quasiconcaveOn_restrictproof · cited by 0