linguistic_hasConfigDim5
plain-language theorem explainer
LinguisticRole satisfies the HasConfigDim5 predicate, confirming its finite cardinality equals 5. Researchers formalizing cross-domain structures in Recognition Science reference this result when assembling the full set of D=5 instances. The proof reduces the claim via unfolding and resolves it through the decide tactic on the derived Fintype instance.
Claim. The inductive type with constructors subject, verb, object, modifier, complement has cardinality 5, i.e., $Fintype.card(LinguisticRole) = 5$.
background
The ConfigDimUniversality module defines HasConfigDim5 (T : Type) [Fintype T] to hold precisely when the cardinality of T equals 5. This predicate formalizes the recurrence of five-element structures across sensory, emotional, biological, economic, and linguistic domains. LinguisticRole is defined inductively with exactly those five constructors and derives the required Fintype instance.
proof idea
Unfold HasConfigDim5 reduces the goal to Fintype.card LinguisticRole = 5. The decide tactic then evaluates the cardinality directly from the inductive definition and its derived Fintype instance.
why it matters
This theorem supplies one of the five entries in configDimUniversalityCert. It is invoked in five_domain_product to establish the product cardinality 3125. Within the Recognition Science framework it instantiates the cross-domain D=5 universality documented in the module's wave-63 audit, independent of the core forcing chain steps T0 through T8.
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