oceanLayerCount
plain-language theorem explainer
oceanLayerCount establishes that the finite type of ocean layers has cardinality exactly 5, matching the five canonical divisions used in Earth science. Recognition Science models of planetary stratification cite this result when assembling the total count of 15 layers across atmosphere, Earth, and ocean. The proof is a direct decision procedure on the Fintype instance derived from the inductive definition.
Claim. Let OceanLayer be the inductive type with constructors surface, thermocline, intermediate, deep, abyssal. Then the cardinality of OceanLayer equals 5.
background
The Oceanography from RS module states that five canonical ocean layers (surface, thermocline, intermediate, deep, abyssal) equal configDim D = 5, with ocean depth following the phi-ladder of recognition density. The inductive type OceanLayer enumerates these five cases and derives DecidableEq, Repr, BEq, Fintype, so its cardinality is immediately computable. This local setting supplies the oceanic component for coupled axes and strata certificates in the broader Recognition Science treatment of planetary structure.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the automatically derived Fintype instance on the five-constructor inductive type.
why it matters
This theorem supplies the ocean count to oceanographyCert, oceanAxis, planetStrataCert, and planet_strata_total_15. It realizes configDim D = 5 for oceanic strata, completing the sum of 15 layers (five each for atmosphere, Earth, ocean) and aligning with the five canonical gyres and surface wave periods noted in the module. The result closes one enumeration step in the Recognition Science derivation of Earth science quantities from the phi-ladder.
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