as some of you may already know, I am currently in the process of
resructing Isabelle's definitions of prime numbers. Before these
changes, we had the concept of "multiplicity". This was defined to be
the multiplicity of a prime factor in the prime decomposition of a
natural number or an integer. The multiplicity of a non-prime was
defined to be 0.
I have now created an alternative definition of "multiplicity" which is
simply defined as "the highest power that is still a divisor" (as long
as this is well-defined); e.g. the multiplicity of -4 in 64 would be 3.
I see three possibilities:
1. redefine my "new", more general multiplicity to the "old" multiplicity
2. keep both notions of multiplicity around with different names
3. replace the old multilicity with the new one and adapt all lemmas
Currently, I tend towards the last options. Are there any other opinions
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