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Theorems · Theorem · order theory

Set.insert_eq_self

∀ {α : Type u_1} {s : Set α} {a : α}, insert a s = s ↔ a ∈ s
Defined in
Mathlib.Data.Set.Insert
Cited by
5 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContDiffWithinAt.fderivWithin · cited by 4ContDiffWithinAt.fderivWi…Balanced.interior · cited by 1Balanced.interiorEuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq · cited by 1EuclideanGeometry.cospher…Matroid.IsBasis'.insert_not_indep · cited by 0IsBasis'.insert_not_indepMatroid.IsBase.insert_dep · cited by 0IsBase.insert_depSet · cited by 53352SetSet.insert_eq_selfCITED BYCITES

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.