noble_gas_complete_shell
plain-language theorem explainer
Noble gases satisfy valence electron count equal to period length at shell closure. Modelers of periodic trends and ionization energies cite the equality when connecting chemical observables to the eight-tick ledger. The proof reduces isNobleGas membership to a six-way disjunction on the explicit list and dispatches each case by native decidable equality.
Claim. If $Z$ is a noble gas then the valence electron count of $Z$ equals the length of the period containing $Z$.
background
The PeriodicTable module supplies a zero-parameter scaffold that maps the Recognition Science eight-tick octave onto chemical periods via fixed block offsets and an 8-window neutrality predicate. Noble gases are defined exactly as the atomic numbers where cumulative valence cost returns to neutrality, realized by the concrete list [2, 10, 18, 36, 54, 86]. valenceElectrons Z is the signed distance from the preceding closure while periodLength Z is the full distance to the next closure; the two quantities coincide precisely at closure points.
proof idea
The term proof first unfolds isNobleGas and nobleGasZ to obtain membership in the fixed list, then simplifies the membership predicate to a disjunction of six equalities. It performs case analysis via obtain rfl on each possibility and resolves every branch by native_decide.
why it matters
The equality is invoked directly by noble_max_ionization to prove that ionizationProxy Z equals periodLength Z for noble gases. It instantiates the Noble Gas Closure Theorem (P0-A0) stated in the module documentation, thereby linking observable shell closures to the 8-tick neutrality condition of the fundamental RS scheduler and to the T7 octave landmark.
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