Theorems · Theorem · order theory
Finset.subset_union_left
∀ {α : Type u_1} [inst : DecidableEq α] {s₁ s₂ : Finset α}, s₁ ⊆ s₁ ∪ s₂- Defined in
- Mathlib.Data.Finset.Lattice.Basic
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 56 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.mem_union_leftproof · cited by 15
Cited by59
Results whose statement or proof uses this declaration.
- Finsupp.sum_add_indexproof · cited by 18
- MeasureTheory.lintegral_tsumproof · cited by 12
- linearIndependent_iff'ₛproof · cited by 9
- finprod_mul_distribproof · cited by 8
- Finsupp.prod_add_indexproof · cited by 6
- multipliable_one_add_of_summableproof · cited by 4
- finsum_add_distribproof · cited by 4
- affineIndependent_iff_indicator_eq_of_affineCombination_eqproof · cited by 4
- SummationFilter.comap_unconditionalproof · cited by 4
- Finset.union_subset_leftproof · cited by 4
- MeasureTheory.inter_mem_measurableCylindersproof · cited by 3
- Finpartition.equitabilise_auxproof · cited by 3