TorchLean API

NN.Floats.Interval.ERealCoercions

Coercion lemmas for ℝ → EReal #

Several IEEE32Exec interval soundness proofs move between real bounds (proved in ) and overflow-safe endpoint reasoning (done in EReal).

This file centralizes small “coe distributes over min/max” rewrite lemmas for the interval soundness modules.

We do not mark these as simp lemmas: they are intended for targeted rewriting in interval proofs, and we want to avoid surprising simp behavior in unrelated developments.

theorem TorchLean.Floats.Interval.coe_min (a b : ) :
(min a b) = min a b

Coercion distributes over min for reals embedded into EReal.

theorem TorchLean.Floats.Interval.coe_max (a b : ) :
(max a b) = max a b

Coercion distributes over max for reals embedded into EReal.