Theorems · Theorem · order theory
Set.iUnion_const
∀ {β : Type u_2} {ι : Sort u_5} [Nonempty ι] (s : Set β), ⋃ x, s = s- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.iUnionstatement · cited by 2,483
- iSup_constproof · cited by 13
Cited by11
Results whose statement or proof uses this declaration.
- IsCompact.nhdsSet_basis_uniformityproof · cited by 4
- isCountablySpanning_measurableSetproof · cited by 3
- MeasurableSpace.generateMeasurableRec_monoproof · cited by 3
- generateFrom_pi_eqproof · cited by 1
- AddCircle.coe_real_preimage_closedBall_eq_iUnionproof · cited by 1
- Measure.ext_of_lintegral_prod_mul_prod_boundedContinuousFunctionproof · cited by 1
- Matroid.IsBasis.isBasis_iUnionproof · cited by 1
- IsCompact.isSigmaCompactproof · cited by 1
- hasSeparatingCovers_iff_separatedNhdsproof · cited by 1
- Set.iUnion_eq_constproof · cited by 0
- Set.hasSeparatingCover_empty_rightproof · cited by 0