Theorems · Theorem · order theory
Set.sdiff_singleton_ssubset
∀ {α : Type u_1} {s : Set α} {a : α}, s \ {a} ⊂ s ↔ a ∈ s- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 59 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 by4
Results whose statement or proof uses this declaration.
- Matroid.IsCircuit.sdiff_singleton_indepproof · cited by 5
- Matroid.IsCircuit.inter_isCocircuit_ne_singletonproof · cited by 2
- Matroid.indep_iff_forall_closure_ssubset_of_ssubsetproof · cited by 0
- Set.diff_singleton_ssubsetproof · cited by 0