Theorems · Theorem · order theory
Set.insert_sdiff_of_mem
∀ {α : Type u_1} {t : Set α} {a : α} (s : Set α), a ∈ t → insert a s \ t = s \ t- Defined in
- Mathlib.Order.BooleanAlgebra.Set
- Cited by
- 22 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 by22
Results whose statement or proof uses this declaration.
- Set.insert_sdiff_self_of_notMemproof · cited by 9
- Set.pair_sdiff_leftproof · cited by 4
- ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithinproof · cited by 3
- LinearIndepOn.notMem_span_of_insertproof · cited by 2
- Affine.Triangle.altitude_eq_mongePlaneproof · cited by 2
- WellFoundedGT.finite_of_sSupIndepproof · cited by 2
- Affine.Simplex.affineSpan_pair_eq_altitude_iffproof · cited by 2
- Matroid.IsBase.isBase_insert_sdiff_of_mem_closureproof · cited by 2
- Matroid.Indep.indep_insert_sdiff_of_mem_closureproof · cited by 2
- exists_sSupIndep_disjoint_sSup_atomsproof · cited by 2
- Matroid.Indep.insert_isCircuit_of_forallproof · cited by 2
- Matroid.Indep.mem_fundCircuit_iffproof · cited by 1