AdditiveDefect
plain-language theorem explainer
The AdditiveDefect inductive type enumerates five canonical defect classes in additive manufacturing, fixed to configDim D = 5 in the Recognition Science materials model. Materials physicists and 3D printing analysts cite this enumeration when classifying volumetric, interlayer, vapor-cavity, mechanical, and boundary defects in metal or polymer prints. The definition lists the five constructors explicitly and derives decidable equality together with finite cardinality structure automatically.
Claim. Let $D=5$ denote the configuration dimension. The set of additive manufacturing defects is the finite enumerated set $S = $ {porosity, lack of fusion, keyhole void, residual stress, surface roughness}, equipped with decidable equality and cardinality $|S|=5$.
background
The module Additive Manufacturing Defects from configDim introduces a discrete classification of defects in additive manufacturing processes. configDim D parametrizes the number of canonical defect classes, here fixed at D=5. The five classes cover volumetric defects (porosity), interlayer defects (lack of fusion), vapor-cavity defects (keyhole voids), mechanical defects (residual stress), and boundary defects (surface roughness) for both metal and polymer printing. This supplies the underlying finite set for all subsequent defect-counting and certification constructions in the module.
proof idea
The declaration is an inductive definition that introduces exactly five constructors, one for each defect class. Derivation clauses then install DecidableEq, Repr, BEq, and Fintype instances automatically.
why it matters
This definition supplies the finite set required by the downstream theorem additiveDefect_count, which proves the cardinality equals 5, and by the structure AdditiveManufacturingDefectsCert, which records the same cardinality fact. It directly encodes the five defect classes stated in the module documentation for the configDim = 5 case. The construction anchors the Recognition Science treatment of materials by providing a discrete, finite classification aligned with the five-dimensional configuration space.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.