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Theorems · Theorem · order theory

Finset.coe_union

∀ {α : Type u_1} [inst : DecidableEq α] (s₁ s₂ : Finset α), ↑(s₁ ∪ s₂) = ↑s₁ ∪ ↑s₂
Defined in
Mathlib.Data.Finset.Lattice.Basic
Cited by
78 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.image₂_union_left · cited by 10Finset.image₂_union_leftFinset.image₂_union_right · cited by 10Finset.image₂_union_rightEquiv.Finset.union · cited by 9Finset.unionfinprod_mul_distrib · cited by 8finprod_mul_distribFinset.Ico_union_Ico_eq_Ico · cited by 7Finset.Ico_union_Ico_eq_I…Submodule.fg_of_fg_map_of_fg_inf_ker · cited by 7Submodule.fg_of_fg_map_of…Algebra.EssFiniteType.comp · cited by 7EssFiniteType.compSubmodule.mem_span_finite_of_mem_span · cited by 6Submodule.mem_span_finite…Finset.image₂_inter_union_subset_union · cited by 6Finset.image₂_inter_union…Finset.image₂_union_inter_subset_union · cited by 6Finset.image₂_union_inter…MvPolynomial.mem_range_map_iff_coeffs_subset · cited by 5MvPolynomial.mem_range_ma…List.support_formPerm_le' · cited by 5List.support_formPerm_le'CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup · cited by 4CompleteLattice.isCompact…finsum_add_distrib · cited by 4finsum_add_distribisPiSystem_piiUnionInter · cited by 3isPiSystem_piiUnionInterSet · cited by 53352SetFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeSet.ext · cited by 2266Set.extFinset.mem_union · cited by 49Finset.mem_unionFinset.coe_unionCITED BYCITES

Cites5

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Cited by79

Results whose statement or proof uses this declaration.