Theorems · Theorem · logic and foundations
Set.Countable.union
∀ {α : Type u} {s t : Set α}, s.Countable → t.Countable → (s ∪ t).Countable- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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.Countablestatement and proof · cited by 545
- Set.countable_unionproof · cited by 2
Cited by16
Results whose statement or proof uses this declaration.
- Set.Countable.of_sdiffproof · cited by 4
- MonotoneOn.countable_not_continuousWithinAtproof · cited by 3
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- Dense.exists_countable_dense_subset_bot_topproof · cited by 3
- MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRingproof · cited by 2
- Set.Countable.isPathConnected_compl_of_one_lt_rankproof · cited by 2
- countable_setOfPred_isolated_rightproof · cited by 2
- exists_countable_union_perfect_of_isClosedproof · cited by 1
- MeasureTheory.countable_generateSetAlgebraproof · cited by 1
- Besicovitch.exists_closedBall_covering_tsum_measure_leproof · cited by 1
- ZMod.completedLFunction_one_sub_evenproof · cited by 1