Formula-phase space bound for one direct transition step #
This module follows the exact state, head, and cell formula trajectories and certifies every nested routine against the shared packed-step width envelope.
theorem
Complexity.CircuitUnrolling.Serializer.DirectGenerator.emitStepFormulas_spaceBoundByWidth_internal
{k : ℕ}
(tm : NTM k)
{initialSpace : ℕ → ℕ}
{values : ℕ → BinaryValues WorkCount}
{width : ℕ → ℕ}
(hclean : ∀ (inputLength : ℕ), StepClean (values inputLength))
(hhorizon : ∀ (inputLength : ℕ), 0 < values inputLength Work.horizon)
(henvelope : ∀ (inputLength : ℕ), StepWidthEnvelope tm (values inputLength) (width inputLength))
:
(emitStepFormulas tm).SpaceBoundByWidthAt initialSpace values width
The complete forward formula phase stays within the shared width envelope.