TorchLean API

FloatLib.Kernels.IntegerRoot.Proof

Exactness of seeded integer roots #

The square-root kernel and the seeded Newton iteration both return the floor root, so the dispatcher agrees with Nat.nthRoot in every degree.

theorem FloatLib.Numerics.IntegerRoot.root_eq_nthRoot (degree value : ℕ) :
root degree value = degree.nthRoot value

The seeded implementation computes Nat.nthRoot for every input and degree.