gridStabilityControl_count
The theorem asserts that the type of grid stability controls has exactly five elements. Researchers working on energy system models within Recognition Science would reference this result when verifying the completeness of grid control sets under the configDim constraint. The proof proceeds via a single application of the decide tactic, which exhaustively checks the cardinality by enumerating the five inductive constructors.
claimThe finite set of grid stability controls, whose elements are inertia, primary frequency response, voltage support, demand response, and storage dispatch, has cardinality five.
background
The module defines five canonical electric-grid stability controls corresponding to configDim D = 5: inertia for rotational buffer, primary frequency response for fast governor action, voltage support for reactive power, demand response for load-side adjustments, and storage dispatch for temporal shifting. The inductive type enumerates these cases and automatically derives Fintype, DecidableEq, Repr, and BEq instances. This setup provides the local theoretical setting for certifying grid stability mechanisms in the Recognition framework.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the statement that the cardinality equals five. The tactic succeeds because the type is a small finite inductive with five explicit constructors, allowing direct computation of the cardinality without additional lemmas.
why it matters in Recognition Science
This result populates the five_controls field in the downstream GridStabilityControlsCert definition, certifying the control set for energy systems. It instantiates the configDim = 5 choice in the grid stability context, consistent with the framework's dimensional assignments such as D = 3 for space. The declaration closes a simple enumeration step without touching open questions in the forcing chain.
scope and limits
- Does not derive these controls from the J-uniqueness or Recognition Composition Law.
- Does not prove stability under specific physical perturbations or load profiles.
- Does not extend to dynamic or time-dependent control counts.
Lean usage
def gridStabilityControlsCert : GridStabilityControlsCert where five_controls := gridStabilityControl_countformal statement (Lean)
27theorem gridStabilityControl_count :
28 Fintype.card GridStabilityControl = 5 := by decide
proof body
29