(computability and complexity): Defining a new kind of reduction: a reduction in log-logarithmic space. for it, let's define a log-logarithmic transformer that is identical to a logarithmic transformer, but it's working tape can hold O(log(logn) symbols and not O(logn) symboles.

We'll say a language A can be reduced in a log-logarithmic space to language B and denote A _LLB, if exists a transformer with log-logarithmic space that applies a mapping reduction between A to B.

Language C will be called P-complete in regards to reduction in log-logarithmic space if:

A)C belongs to class P B)For every language A in P exists a reduction in log-logarithmic space to C(meaning A _LL C).

Prove: A P-Complete language in regards to a log-logarithmic space CANNOT exist.

please provide a proof in academic level please, so i can learn from it. thank you very much