These proofs are mainly by Florian Kammüller. (Later, Larry Paulson simplified some of the proofs.) These theories were indeed the original motivation for locales. Here is an outline of the directory's contents:
Group defines semigroups, monoids,
groups, commutative monoids, commutative groups, homomorphisms and the
subgroup relation. It also defines the product of two groups
(This theory was reimplemented by Clemens Ballarin).
FiniteProduct extends
commutative groups by a product operator for finite sets (provided by
Clemens Ballarin).
Coset defines
the factorization of a group and shows that the factorization a normal
subgroup is a group.
Bij
defines bijections over sets and operations on them and shows that they
are a group. It shows that automorphisms form a group.
Exponent the
combinatorial argument underlying Sylow's first theorem.
Sylow
contains a proof of the first Sylow theorem.
CRing
defines Abelian monoids and groups. The difference to commutative
structures is merely notational: the binary operation is
addition rather than multiplication. Commutative rings are
obtained by inheriting properties from Abelian groups and
commutative monoids. Further structures in the algebraic
hierarchy of rings: integral domain.
Module
introduces the notion of a R-left-module over an Abelian group, where
R is a ring.
UnivPoly
constructs univariate polynomials over rings and integral domains.
Degree function. Universal Property.
A development of univariate polynomials for HOL's ring classes
is available at HOL/Library/Polynomial.
[Jacobson1985] Nathan Jacobson, Basic Algebra I, Freeman, 1985.
[Ballarin1999] Clemens Ballarin, Computer Algebra and Theorem Proving, Author's PhD thesis, 1999. Also University of Cambridge, Computer Laboratory Technical Report number 473.