assessmentType_count
The theorem establishes that the inductive type of canonical assessment types has finite cardinality exactly 5. Education researchers applying the Recognition Science model to curriculum design would cite this result when fixing the number of assessment modalities to match configDim D = 5. The proof is a direct decision procedure on the automatically derived Fintype instance of the inductive definition.
claimThe finite cardinality of the inductive type consisting of the five constructors diagnostic, formative, summative, criterion-referenced, and portfolio equals 5.
background
The module models educational assessment as an inductive type with five variants that span the practical cycle: baseline evaluation, ongoing feedback, final certification, standard alignment, and longitudinal artifact collection. These variants are declared to correspond directly to the configDim parameter fixed at D = 5. The upstream inductive definition supplies the constructors and derives the DecidableEq, Repr, BEq, and Fintype instances used by the cardinality statement.
proof idea
The proof is a one-line wrapper that applies the decide tactic to evaluate the cardinality computation on the Fintype instance derived from the inductive type.
why it matters in Recognition Science
This result populates the five_types field inside the AssessmentTypesCert definition, anchoring the education module to the configDim = 5 convention. It supplies a concrete count that downstream certification objects rely on when embedding assessment structure into the broader Recognition Science framework.
scope and limits
- Does not derive the five types from the J-function or Recognition Composition Law.
- Does not connect assessment types to spatial dimensions or physical constants.
- Does not prove that these five modalities are optimal or exhaustive.
Lean usage
def cert : AssessmentTypesCert := { five_types := assessmentType_count }formal statement (Lean)
26theorem assessmentType_count : Fintype.card AssessmentType = 5 := by decide
proof body
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