Commit 2024-05-09 04:14 47d4fa91

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feat(Algebra/Ring/Ext): prove extensionality lemmas for Ring and similar typeclasses (#9511) Add a file Algebra/Ring/Ext, proving ext lemmas for all of the ring-like classes (for example, anything from NonUnitalNonAssocSemiring to CommRing), stating that two instances of such a class are equal if they define the same addition and multiplication operations. Also prove ext_iff variants for each class, and injectivity lemmas for projections from classes to parent classes.

Estimated changes

added theorem AddGroupWithOne.ext
added theorem AddMonoidWithOne.ext
added theorem CommRing.ext
added theorem CommRing.ext_iff
added theorem CommSemiring.ext
added theorem CommSemiring.ext_iff
added theorem Distrib.ext
added theorem Distrib.ext_iff
added theorem NonAssocRing.ext
added theorem NonAssocRing.ext_iff
added theorem NonAssocSemiring.ext
added theorem NonUnitalCommRing.ext
added theorem NonUnitalRing.ext
added theorem NonUnitalRing.ext_iff
added theorem NonUnitalSemiring.ext
added theorem Ring.ext
added theorem Ring.ext_iff
added theorem Semiring.ext
added theorem Semiring.ext_iff