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chore(RingTheory/Ideal): add new file `Ideal.IsPrincipal`
This PR adds a new file RingTheory.Ideal.IsPrincipal and moves most of the (basic) results about Ideal.IsPrincipal and Ideal.span_singleton from Ideal.Basic and Ideal.Operations to this file. (Some very basic results or results related to Submodule.span_singleton are left in place.)
The need for this PR comes from a discussion in #12780 about where to put the proof that the equivalence between principal ideals and associates is actually a MulEquiv (#13177).
Some remarks:
no_lost_declarations.shsays
* 25 added declarations
* 25 removed declarations
* 5 paired declarations
this is due to some renames in the variables and also namespace changes. I have checked that the added declarations correspond exactly to the removed declarations
- Some results that could not stay in
Ideal.Basicbut are not really related to principal ideals have been moved (for the moment?) to the end ofIdeal.IsPrincipal(see themiscsection). I thought about putting them inIdeal.Operationsbut the file is already quite large (about 1400 lines). Note thatIdeal.OperationsimportsIdeal.IsPrincipaland these additional results do not add any extra import toIdeal.IsPrincipal. Still, they should probably go somewhere else...