[Merged by Bors] - feat(Topology/Bases): review IsSeparable API
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urkud
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* upgrade `isSeparable_iUnion` to an `Iff` lemma, restore the original version as `IsSeparable.iUnion`; * add `isSeparable_union` and `isSeparable_closure`; * upgrade `isSeparable_pi` from `[Finite ι]` to `[Countable ι]`, add `IsSeparable.univ_pi` version; * add `Dense.isSeparable_iff` and `isSeparable_range`; * rename `isSeparable_of_separableSpace_subtype` to `IsSeparable.of_subtype`; * rename `isSeparable_of_separableSpace` to `IsSeparable.of_separableSpace`.
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IsSeparable APIIsSeparable API
atarnoam
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* upgrade `isSeparable_iUnion` to an `Iff` lemma, restore the original version as `IsSeparable.iUnion`; * add `isSeparable_union` and `isSeparable_closure`; * upgrade `isSeparable_pi` from `[Finite ι]` to `[Countable ι]`, add `IsSeparable.univ_pi` version; * add `Dense.isSeparable_iff` and `isSeparable_range`; * rename `isSeparable_of_separableSpace_subtype` to `IsSeparable.of_subtype`; * rename `isSeparable_of_separableSpace` to `IsSeparable.of_separableSpace`.
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isSeparable_iUnionto anIfflemma, restore the original version asIsSeparable.iUnion;isSeparable_unionandisSeparable_closure;isSeparable_pifrom[Finite ι]to[Countable ι], addIsSeparable.univ_piversion;Dense.isSeparable_iffandisSeparable_range;isSeparable_of_separableSpace_subtypetoIsSeparable.of_subtype;isSeparable_of_separableSpacetoIsSeparable.of_separableSpace.