tier_power_positive
plain-language theorem explainer
The theorem establishes that the lower power bound for every Nautilus tier exceeds zero. Engineers modeling Class C technological access would cite it when verifying tier feasibility. The proof proceeds by exhaustive case analysis on the three tiers followed by simplification and numerical normalization.
Claim. For every Nautilus tier $t$, let $(L, U)$ be the power range assigned to $t$. Then $L > 0$.
background
NautilusTier is the inductive type with three constructors: quietRoom (10-100 W meditation amplifier), temple (5-10 kW healing field), and ignition (>100 kW pulsed metric editing). tierPowerRange is the function that maps each constructor to its explicit wattage interval. The module formalizes the Nautilus-class technological access path for Class C powers, treating power tiers and mappings as model definitions.
proof idea
The proof performs case analysis on the three constructors of NautilusTier. Each case simplifies via the explicit definition of tierPowerRange and applies norm_num to confirm the lower bound is positive.
why it matters
The declaration secures the positivity of lower power bounds within the Nautilus tier model. It underpins the power-to-tier mapping used for Class C superhuman capabilities. The module treats these as structural definitions separate from proved physical claims.
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