Theorems · Theorem · order theory
Set.sdiff_singleton_eq_self
∀ {α : Type u_1} {s : Set α} {a : α}, a ∉ s → s \ {a} = s- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- sdiff_eq_self_iff_disjointproof · cited by 4
Cited by38
Results whose statement or proof uses this declaration.
- Set.insert_sdiff_singleton_commproof · cited by 7
- Matroid.IsCircuit.closure_sdiff_singleton_eqproof · cited by 5
- Set.pair_sdiff_leftproof · cited by 4
- hasDerivWithinAt_iff_tendsto_slope'proof · cited by 4
- Set.wcovBy_insertproof · cited by 4
- Matroid.isColoop_tfaeproof · cited by 4
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- isClosed_iff_derivedSet_subsetproof · cited by 3
- ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interiorproof · cited by 2
- ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interiorproof · cited by 2
- LinearIndepOn.notMem_span_of_insertproof · cited by 2