Generation
plain-language theorem explainer
The declaration supplies the natural numbers as carrier for generation counts in a minimal biological model of the forcing chain. Researchers extending particle generation structures to reproductive dynamics cite it when composing ledger entries with biologyCost. The alias reuses the standard Nat type with no added axioms or structure.
Claim. In the lightweight biological realization the carrier for generation counts is the set of natural numbers, with the successor operation serving as the reproductive generator.
background
The BiologyRealization module supplies a minimal model in which biological processes are carried by generation counts. The reproductive step functions as the generator on this carrier, consistent with the module's stated purpose of a lightweight realization.
proof idea
The definition is a direct abbreviation to the built-in natural numbers type. No lemmas or tactics are invoked; the alias simply re-exports Nat for use as the generation carrier.
why it matters
This carrier feeds the sibling declarations biologyCost and biologyInterpret, which in turn appear in ConstantsAudit and GaugeFromCube. It supports the extension of the three-generations result from D = 3 (see three_generations_from_dimension) into biological scales while preserving the cube geometry underlying the eight-tick octave.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.