ORMethod
plain-language theorem explainer
The inductive type ORMethod enumerates the five canonical operations research techniques as linear programming, dynamic programming, game theory, queuing theory, and simulation. Applied mathematicians and economists mapping standard OR techniques onto Recognition Science would cite this enumeration when treating optimization as J-cost minimization with configuration dimension D equal to 5. The definition proceeds by direct inductive construction of the type together with automatic derivation of the Fintype instance.
Claim. Let ORMethod be the inductive type whose five constructors are linear programming, dynamic programming, game theory, queuing theory, and simulation. In the Recognition Science setting this type indexes the methods for minimizing J-cost over the decision space, where the optimal solution satisfies J = 0.
background
The module Operations Research from RS treats optimization as minimization of J-cost over the decision space, with the optimal solution defined by J = 0. J-cost is the recognition cost function imported from the Cost module and obeying the Recognition Composition Law. The five listed methods are identified with the configuration dimension D set to 5.
proof idea
The declaration is the inductive definition of the type with exactly five constructors. Deriving clauses attach DecidableEq, Repr, BEq, and Fintype instances with no additional proof obligations. No lemmas or tactics are invoked; the definition stands alone.
why it matters
This definition supplies the type required by OperationsResearchCert to assert both that the cardinality equals 5 and that the optimal J-cost is zero. It maps the standard operations research techniques onto the Recognition Science framework in which optimization reduces to J-cost minimization. The construction supports the claim that these five methods correspond to the D = 5 configuration space.
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