TorchLean API

NN.Floats.IEEEExec.NatLemmas

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:

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.