br_dist_one
plain-language theorem explainer
The declaration asserts that bromine at atomic number 35 lies exactly one step short of the next noble-gas closure. Chemists applying Recognition Science shell scaling would cite this to anchor halogen positions on the phi-ladder. The proof is a one-line native_decide evaluation of the closure-distance definition.
Claim. The distance to the next noble-gas shell closure for atomic number 35 equals 1, where the distance is defined as the difference between the atomic number of the subsequent noble gas and the current atomic number.
background
Atomic radii in this module follow phi-ladder scaling with shell number and screening: radii decrease across a period as nuclear charge increases and increase down a group as new shells appear. Noble gases mark local maxima because they complete shells. The upstream definition distToNextClosure(Z) returns the steps to the next closure and equals zero precisely at noble gases, counting valence electrons beyond the prior closed shell.
proof idea
The proof is a one-line wrapper that applies native_decide to evaluate the arithmetic definition of distToNextClosure at input 35.
why it matters
This fact verifies the shell-closure count for bromine immediately before krypton, supporting the module's period and group trends derived from phi-ladder coherence lengths. It fills a concrete check in the CH-007 atomic-radii predictions without yet feeding any recorded downstream theorems. The result remains isolated until explicit radius formulas are linked to the closure distances.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.