additiveDefect_count
plain-language theorem explainer
The result fixes the number of canonical additive manufacturing defect classes at five under the configDim parameterization. Materials modelers and 3D-printing physicists would cite the count when setting the discrete dimension for defect certification. The proof is a direct decision on the Fintype instance of the five-constructor inductive type.
Claim. The finite set of canonical additive-manufacturing defects has cardinality five: $|A| = 5$, where $A$ consists of porosity, lack-of-fusion, keyhole voids, residual stress, and surface roughness.
background
The module AdditiveManufacturingDefectsFromConfigDim defines five defect classes tied to configDim set to 5. These are introduced via the inductive type whose constructors are porosity, lackOfFusion, keyholeVoid, residualStress, and surfaceRoughness, each deriving DecidableEq, Repr, BEq, and Fintype. The local setting supplies a certified defect count for the materials sector, resting on the upstream inductive enumeration that supplies the Fintype instance.
proof idea
The proof is a one-line wrapper that applies the decide tactic to evaluate the cardinality of the enumerated inductive type.
why it matters
The cardinality supplies the five_defects field inside additiveManufacturingDefectsCert, anchoring the materials defect model. It instantiates configDim = 5 for this domain while remaining consistent with the framework's discrete parameterization steps that follow the eight-tick octave and spatial forcing. No open scaffolding questions are closed here.
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