businessCyclePhaseCount
plain-language theorem explainer
The declaration fixes the number of canonical business cycle phases at five. Economists modeling counter-cyclical policy from the gap-45 would cite this cardinality to anchor the discrete state space. The proof is a one-line decision procedure on the Fintype instance derived from the five-constructor inductive type.
Claim. The set of business cycle phases, consisting of trough, recovery, expansion, peak and contraction, has cardinality five.
background
The module derives counter-cyclical policy from gap-45, identified with the Kondratieff wave. BusinessCyclePhase is introduced as an inductive type whose five constructors are trough, recovery, expansion, peak and contraction, with an automatic Fintype instance. The module states that this count equals configDim D = 5. Upstream gap definitions supply the 45-year scale as the product of closure and Fibonacci factors.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the Fintype instance generated by the inductive definition.
why it matters
This cardinality supplies the five_phases field inside counterCyclicalPolicyCert. It implements the framework claim that business cycle phases number five under configDim D = 5 in the gap-45 economics setting. The result precedes the policy balance condition that relates stimulus and austerity intervals by the inverse golden ratio.
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