Theorems · Theorem · order theory
Set.insert_eq
∀ {α : Type u_1} (x : α) (s : Set α), insert x s = {x} ∪ s- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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 by47
Results whose statement or proof uses this declaration.
- affineSpan_insert_affineSpanproof · cited by 7
- Submodule.span_insertproof · cited by 6
- Set.Ioc_insert_leftproof · cited by 6
- Set.Ico_insert_rightproof · cited by 5
- Set.Ioo_insert_rightproof · cited by 5
- nhdsSet_insertproof · cited by 4
- Set.Icc_sdiff_bothproof · cited by 4
- IsLUB.insertproof · cited by 4
- Set.Ioo_insert_leftproof · cited by 4
- Finset.Ico_insert_rightproof · cited by 3
- lowerBounds_insertproof · cited by 3
- IsGLB.insertproof · cited by 3