Theorems · Theorem · order theory
Partition.subset_sUnion_and_mem_iff_mem
∀ {α : Type u_1} {S : Set (Set α)} {u t : Set α} {P : Partition u}, S ⊆ ↑P → (t ⊆ ⋃₀ S ∧ t ∈ P ↔ t ∈ S)- Defined in
- Mathlib.Order.Partition.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SetLike.coestatement and proof · cited by 8,199
- Set.sUnionstatement and proof · cited by 392
- Partitionstatement and proof · cited by 91
- Set.subset_sUnion_of_memproof · cited by 39
- Partition.eq_of_mem_of_memproof · cited by 5
- Partition.nonempty_of_memproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Partition.subset_sUnion_iff_memproof · cited by 0