nanostructureTypeCount
plain-language theorem explainer
The declaration asserts that the finite set of nanostructure types contains exactly five members. A materials physicist working within the Recognition Science derivation of nanoscale phenomena would cite this cardinality when verifying the completeness of the canonical list. The proof proceeds by a single decide tactic that exhausts the inductive constructors.
Claim. The cardinality of the set of nanostructure types is five: $|$ {nanoparticle, nanowire, nanosheet, nanotube, quantum dot} $| = 5$.
background
In the NanoScienceFromRS module, nanoscale phenomena arise from recognition at the Q₃ lattice spacing with unit cell a₀. The inductive type NanostructureType enumerates five canonical forms: nanoparticle, nanowire, nanosheet, nanotube, and quantum dot. This count aligns with configDim D = 5 as stated in the module documentation for E2/B10 materials.
proof idea
The proof is a one-line wrapper that applies the decide tactic to compute Fintype.card on the inductive type NanostructureType.
why it matters
This result supplies the five_structures field in the nanoScienceCert definition, completing the certification that nanoscale structures match the five-phenomena count. It instantiates the configDim D = 5 landmark from the Recognition Science framework for nanoscience applications.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.