Theorems · Theorem · order theory
Set.ofPred_exists
∀ {β : Type u_2} {ι : Sort u_5} (p : ι → β → Prop), {x | ∃ i, p i x} = ⋃ i, {x | p i x}- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredstatement · cited by 6,101
- Set.iUnionstatement · cited by 2,483
- Set.extproof · cited by 2,266
- Set.mem_iUnionproof · cited by 212
Cited by23
Results whose statement or proof uses this declaration.
- ProbabilityTheory.setBernoulli_ae_subsetproof · cited by 5
- MeasureTheory.measurableSet_exists_tendstoproof · cited by 4
- MeasureTheory.measure_setOfPred_frequently_eq_zeroproof · cited by 3
- IsOpen.relImageproof · cited by 3
- finite_memPartitionproof · cited by 3
- Measurable.isLUBproof · cited by 3
- measurableSet_of_differentiableAt_of_isComplete_with_paramproof · cited by 2
- volume_iUnion_setOfPred_liouvilleWithproof · cited by 2
- ProbabilityTheory.Kernel.setIntegral_densityproof · cited by 2
- Metric.thickening_iUnionproof · cited by 2
- BoxIntegral.IntegrationParams.hasBasis_toFilteriUnionproof · cited by 2
- measurableSet_tendstoproof · cited by 2