properties

Artur Kornilowicz <[email protected]>
Newsgroups gmane.comp.mathematics.mizar
Message-ID <Pine.SOL.4.64.1108101500350.1820@math>
In mathematics there are unary operations (let say f) satisfying property

f^m(x) = f^n(x).

Some of them have commonly used names, like

for m = 2, n = 1, that is f(f(x)) = f(x) - projectivity

for m = 2, n = 0, that is f(f(x)) = x - involutiveness



In the MML there are theorems about operations satisfying the property
for m = 1 and n = 0, for example:

theorem
   for m being Nat holds m = abs m

theorem
  for T being non empty TopSpace, a being Point of T,
      P being constant Path of a,a
  holds - P = P

We are thinking about implementation of the property (m=1,n=0) in Mizar, 
and we are looking for an appropriate name for it.

Any suggestions?

Best regards
Artur
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