Theorems · Theorem · order theory
Set.union_insert
∀ {α : Type u_1} {s t : Set α} {a : α}, s ∪ insert a t = insert a (s ∪ t)- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 11 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 by11
Results whose statement or proof uses this declaration.
- setOfPred_isPreconnected_subset_of_orderedproof · cited by 2
- algebraicIndependent_of_set_of_finiteproof · cited by 1
- FirstOrder.Language.denselyOrdered_of_dloproof · cited by 1
- FirstOrder.Language.noBotOrder_of_dloproof · cited by 1
- FirstOrder.Language.noTopOrder_of_dloproof · cited by 1
- EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_neproof · cited by 1
- exists_of_linearIndepOn_of_finite_spanproof · cited by 1
- EuclideanGeometry.cospherical_of_mul_dist_eq_mul_dist_of_angle_eq_piproof · cited by 0
- eVariationOn.union'proof · cited by 0
- AffineIndependent.not_wbtw_of_injectiveproof · cited by 0