Theorems · Theorem · order theory
Set.insert_inter_of_mem
∀ {α : Type u_1} {s t : Set α} {a : α}, a ∈ t → insert a s ∩ t = insert a (s ∩ t)- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by5
Results whose statement or proof uses this declaration.
- Order.Ico_succ_right_eq_insert_of_not_isMaxproof · cited by 2
- Order.Ioc_pred_left_eq_insert_of_not_isMinproof · cited by 1
- Order.Ioo_succ_right_eq_insert_of_not_isMaxproof · cited by 1
- Matroid.mem_closure_insertproof · cited by 1
- Order.Ioo_pred_left_eq_insert_of_not_isMinproof · cited by 1