field-extensions's Introduction

field-extensions

Field Extensions in HOL-Algebra – an interdisciplinary verification project based on Isabelle2019.

The theories in VectorSpace_by_HoldenLee/ stem from the Archive of Formal Proofs (AFP), cf. https://devel.isa-afp.org/entries/VectorSpace.html and https://devel.isa-afp.org/browser_info/current/AFP/Jordan_Normal_Form/Missing_VectorSpace.html. I have slightly adjusted them to better use the new HOL-Algebra:

In RingModuleFacts.thy, I removed the now-superseded facts lmult_0 and rmult_0, and the constant units_group, which duplicates Group.units_of.
In MonoidSums, finprod_all1 is superseded by finprod_one_eqI. The lemmas factors_equal/summands_equal are trivial and unused in the AFP.
In LinearCombinations, I replaced the definition submodule by Module.submodule. Careful: The latter does not assume the superstructure to be a module. This may affect statements in descendant theories. Moreover, I needed to adjust the argument order. (The converse change, namely adjusting Module.submodule's argument order, might have been the easier way in retrospect.) Furthermore, I removed some confusing junk from within the definition of func_space.
In SumSpaces, I once again clarified a definition. I also slightly relaxed the type constraint on inj1 and inj2, one could further relax it to ring_scheme.
In VectorSpace, I removed two superseded lemmas and changed the premise of func_space_is_vs to make it consistent with ring.func_space_is_module.
In Missing_VectorSpace, I removed vectorspace.lincomb_distrib which is just the symmetric of LinearCombinations.module.lincomb_smult.