polymerMorphology_count
plain-language theorem explainer
The declaration establishes that the inductive type of polymer morphologies contains exactly five elements. Materials scientists mapping block-copolymer phases to the phi-ladder would reference this cardinality when classifying observed structures. The proof reduces to a single decide tactic that computes the Fintype cardinality from the five constructors.
Claim. The finite set of canonical polymer morphologies has cardinality five: $|PolymerMorphology| = 5$.
background
The module defines five canonical block-copolymer morphologies corresponding to configDim equal to five. These are spherical, cylindrical, gyroid, lamellar, and inverseMorph, each tied to a distinct minority-block volume-fraction band on the phi-ladder. The upstream inductive definition lists the constructors without additional hypotheses.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the Fintype.card expression for the inductive type.
why it matters
This count populates the polymerMorphologyCert definition, which certifies the five morphologies in the Chemistry module. It aligns with the Recognition Science claim of five morphologies from configDim D=5, linking to the phi-ladder volume fractions.
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