Theorems · Theorem · logic and foundations
Set.sep_subset
∀ {α : Type u} (s : Set α) (p : α → Prop), {x | x ∈ s ∧ p x} ⊆ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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.ofPredstatement · cited by 6,101
Cited by16
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.congr_of_eventuallyEqproof · cited by 9
- TopologicalSpace.isOpen_iUnion_countableproof · cited by 9
- setOfPred_minimal_subsetproof · cited by 5
- SimpleGraph.isBipartiteWith_neighborSet_subsetproof · cited by 3
- IsAddIndecomposable.subsetproof · cited by 2
- IsCompact.extremePoints_nonemptyproof · cited by 2
- IsCompact.finite_sdiff_of_mem_codiscreteWithinproof · cited by 2
- ChainCompletePartialOrder.IsExtremePt.bot_eq_of_le_or_map_leproof · cited by 2
- exists_countable_union_perfect_of_isClosedproof · cited by 1
- setOfPred_maximal_subsetproof · cited by 1
- SimpleGraph.isBipartiteWith_neighborSet_subset'proof · cited by 1
- TopologicalSpace.exists_isInducing_l_inftyproof · cited by 1