Exponential of base 2: Definition and properties

Definition

We define the function two_power with the Recursive feature:
Recursive Definition two_power:nat->nat:=
            O => (S O)
          | (S n) => (mult two (two_power n)).

Some properties of two_power

We prove some lemmas about two_power, which are mainly used in the module log2 . They state some relationships between this function and the order on natural numbers:

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