Small Nat lemmas for the IEEE32Exec float kernel #
The executable IEEE-754 kernel (NN/Floats/IEEEExec/Exec32.lean) defines a handful of low-level
Nat helpers such as:
pow2 k = 2^k(as aNat), implemented viaNat.shiftLeft.
The IEEEExec bridge and soundness proofs use the same facts about these helpers, so the shared lemmas live here.
pow2 k is just 2^k.
Informal: pow2 is defined as Nat.shiftLeft 1 k, i.e. shifting the bit 1 left by k places,
which equals the power of two 2^k.
pow2 k is strictly positive.
Informal: 2^k > 0 for all k, hence the same holds for pow2 k.