Theorems · Theorem · logic and foundations
Set.Countable.mono
∀ {α : Type u} {s₁ s₂ : Set α}, s₁ ⊆ s₂ → s₂.Countable → s₁.Countable- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Elemproof · cited by 7,166
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- Set.Countable.to_subtypeproof · cited by 33
- Set.inclusion_injectiveproof · cited by 28
- Function.Injective.countableproof · cited by 10
Cited by34
Results whose statement or proof uses this declaration.
- TopologicalSpace.exists_countable_basisproof · cited by 9
- TopologicalSpace.isOpen_iUnion_countableproof · cited by 9
- Set.countable_ofPred_finite_subsetproof · cited by 5
- 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
- Set.countable_iff_exists_subset_rangeproof · cited by 3
- countable_setOfPred_covBy_rightproof · cited by 3
- countable_setOfPred_isolated_right_withinproof · cited by 3
- PMF.toMeasure_apply_eq_toOuterMeasureproof · cited by 3