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 accordingly

Currently, I tend towards the last options. Are there any other opinions on this?


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