Theorems · Theorem · combinatorics
Finset.biUnion_subset
∀ {α : Type u_1} {β : Type u_2} {s : Finset α} {t : α → Finset β} [inst : DecidableEq β] {s' : Finset β},
s.biUnion t ⊆ s' ↔ ∀ x ∈ s, t x ⊆ s'- Defined in
- Mathlib.Data.Finset.Union
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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.
- Finsetstatement and proof · cited by 13,712
- Finset.biUnionstatement · cited by 217
Cited by8
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.support_coeff_mul_subsetproof · cited by 5
- MonoidAlgebra.support_coeff_mul_subsetproof · cited by 3
- SkewMonoidAlgebra.support_mulproof · cited by 2
- Int.erdos_ginzburg_zivproof · cited by 2
- WittVector.remainder_varsproof · cited by 1
- WittVector.wittPolyProdRemainder_varsproof · cited by 1
- Finset.biUnion_sliceproof · cited by 1
- Finset.card_biUnion_le_of_intersectingproof · cited by 0