Theorems · Theorem · logic and foundations
Set.exists_of_ssubset
∀ {α : Type u} {s t : Set α}, s ⊂ t → ∃ x ∈ t, x ∉ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 21 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
- Set.not_subsetproof · cited by 31
Cited by13
Results whose statement or proof uses this declaration.
- SetLike.exists_of_ltproof · cited by 16
- Set.ssubset_iff_of_subsetproof · cited by 9
- Set.ssubset_iff_existsproof · cited by 8
- Matroid.Dep.exists_isCircuit_subsetproof · cited by 5
- Matroid.Indep.exists_insert_of_not_isBaseproof · cited by 5
- Matroid.Indep.closure_ssubset_closureproof · cited by 3
- Set.exists_subset_encard_eqproof · cited by 3
- Matroid.IsCircuit.isBasis_iff_eq_sdiff_singletonproof · cited by 2
- Affine.Simplex.centroid_notMem_affineSpan_of_ne_univproof · cited by 1
- Matroid.Indep.union_indep_iff_forall_notMem_closure_rightproof · cited by 1
- SimpleGraph.maximal_isAcyclic_iff_reachable_eqproof · cited by 1
- AffineSubspace.exists_of_ltproof · cited by 0