classC_has_tier
plain-language theorem explainer
Every power classified as NautilusClass possesses a defined minimum required tier under the Nautilus architecture. Modelers of Class C technological access cite this result to confirm that the tier mapping is total on that subclass. The proof executes exhaustive case analysis on the Power inductive type, after which simplification with the powerClass and requiredTier definitions discharges each goal.
Claim. For every power $p$ satisfying powerClass$(p)=$ NautilusClass, the map requiredTier$(p)$ returns a concrete NautilusTier (i.e., (requiredTier$(p)$).isSome holds).
background
The module encodes the Nautilus-class technological access path for Class C powers. Power is the inductive enumeration of 27 canonical superhuman abilities drawn from mythology, comics, and folklore. The function powerClass partitions these abilities into epistemic classes, placing the relevant constructors into NautilusClass. The companion definition requiredTier then supplies an explicit Option NautilusTier for each such power (flight maps to ignition, invulnerability and superStrength map to temple, etc.).
proof idea
The term proof opens with cases p, splitting on every constructor of the Power inductive type. The subsequent simp_all tactic, supplied with the definitions of powerClass and requiredTier, reduces each resulting subgoal to a reflexivity or true equality.
why it matters
The result supplies the basic existence claim for tier assignment on the NautilusClass, closing the structural model of Class C access before engineering parameters are attached. It sits inside the Nautilus architecture parameters section and inherits the hygiene convention that tier mappings are treated as MODEL definitions. No downstream theorems are recorded, leaving the result as a leaf fact that any larger access-path theorem would invoke.
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