emotion_hasConfigDim5
plain-language theorem explainer
PrimaryEmotion, the inductive type whose five constructors are joy, sadness, fear, anger and disgust, satisfies the predicate that its Fintype cardinality equals five. Researchers assembling product spaces or certifying config-dimension universality across domains cite this instance when building the five-domain certificate or the 125-element triple product. The proof is a one-line wrapper that unfolds the cardinality predicate and lets decide compute the result from the derived Fintype instance.
Claim. Let PrimaryEmotion be the inductive type with constructors joy, sadness, fear, anger, disgust. Then the cardinality of PrimaryEmotion under its Fintype instance equals five: $Fintype.card PrimaryEmotion = 5$.
background
HasConfigDim5 is the predicate asserting that a type T equipped with a Fintype instance has cardinality exactly five. PrimaryEmotion is the inductive type with precisely those five constructors and derives DecidableEq, Repr, BEq and Fintype, making the cardinality decidable. The module formalises the structural claim that config dimension five appears across domains with high frequency, listing five canonical instances whose cardinalities are all proved by decide.
proof idea
The proof is a one-line wrapper. It unfolds HasConfigDim5, reducing the goal to Fintype.card PrimaryEmotion = 5, then applies the decide tactic which evaluates the cardinality directly from the Fintype derivation on the inductive type.
why it matters
This instance populates the configDimUniversalityCert record together with the four other domain instances and supplies the hypothesis for the three-domain product theorem (cardinality 125) and the five-domain product theorem (cardinality 3125). It realises one of the five canonical D=5 domains required by the C13 universality statement in the module documentation.
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