economic_hasConfigDim5
plain-language theorem explainer
EconomicCycle, the inductive type with five phases (recession, recovery, expansion, peak, contraction), satisfies HasConfigDim5, i.e., has cardinality exactly 5. Cross-domain researchers cite this instance when building the universality certificate or the five-domain product of cardinality 3125. The proof is a one-line wrapper that unfolds the predicate and invokes decide on the derived Fintype instance.
Claim. Let $E$ be the inductive type with five constructors recession, recovery, expansion, peak, contraction. Then $Fintype.card E = 5$.
background
HasConfigDim5 (T : Type) [Fintype T] is the predicate that holds exactly when the finite cardinality of T equals 5. EconomicCycle is the self-contained inductive type whose five constructors enumerate the canonical phases of an economic cycle and derives Fintype, DecidableEq, and Repr. The module establishes that configDim D = 5 appears uniformly across five independent domains (sensory, emotional, biological, economic, linguistic) and proves cross-domain consequences such as the 5^5 product cardinality.
proof idea
One-line wrapper that unfolds HasConfigDim5, reducing the goal to Fintype.card EconomicCycle = 5, then applies the decide tactic which succeeds because the inductive type derives Fintype and contains exactly five elements.
why it matters
Feeds directly into configDimUniversalityCert (which assembles the five domain instances) and five_domain_product (which computes the joint cardinality 3125). It instantiates the module's structural claim that D = 5 occurs with overwhelming frequency across domains, complementing the spatial dimension D = 3 obtained from the forcing chain at T8. The proof is complete with zero sorry or axioms.
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