legalTradition_count
plain-language theorem explainer
The theorem establishes that the finite type of legal traditions has cardinality exactly five. Comparative law researchers mapping global systems to Recognition Science configuration spaces would cite it to anchor the D=5 case. The proof is a one-line decision procedure that evaluates the derived Fintype instance on the inductive enumeration of five constructors.
Claim. The set of canonical legal traditions has cardinality five: $|L| = 5$, where $L = $ {civil law, common law, Islamic (sharia), customary, socialist}.
background
Recognition Science assigns five canonical legal traditions to configuration dimension D = 5. The inductive type LegalTradition enumerates them explicitly as civilLaw, commonLaw, islamicSharia, customary, and socialist, each constructor deriving DecidableEq, Repr, BEq, and Fintype instances. The module states that these five cover more than 95 percent of the world's jurisdictions under standard comparative-law classifications.
proof idea
The proof is a one-line wrapper that applies the decide tactic. This tactic computes the cardinality directly from the Fintype instance automatically generated by the inductive definition of LegalTradition.
why it matters
The result supplies the integer value required by the downstream definition legalTraditionsCert, which packages the cardinality into a certified structure. It realizes the module claim that configDim D = 5 produces exactly these five traditions, linking the Recognition Science forcing chain (T7 eight-tick octave and D = 3 spatial base extended to higher dimensions) to empirical jurisprudence. No open scaffolding questions are indicated.
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