[isabelle-dev] multiplicity and prime numbers

Tobias Nipkow nipkow at in.tum.de
Tue Jul 19 12:18:07 CEST 2016

Are you sure that there is no standard definition of this concept in mathematics 
that we should follow?


On 19/07/2016 12:03, Manuel Eberl wrote:
> Hallo,
> 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?
> Cheers,
> Manuel
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