ethicsCost_self
plain-language theorem explainer
ethicsCost_self establishes that the cost of comparing any moral improvement step to itself is zero. Workers on the universal forcing chain cite it to confirm the zero element in the ethical carrier. The proof reduces directly via simplification of the ethicsCost definition.
Claim. Let ethicsCost be the function on natural numbers given by ethicsCost(a,b) = 0 if a = b and 1 otherwise. Then for every natural number a, ethicsCost(a,a) = 0.
background
The EthicsRealization module supplies a lightweight formalization of ethical realization for the Universal Forcing framework. MoralImprovementStep is defined as the natural numbers and serves as the carrier that counts morally meaningful improvement steps. The module does not rebuild a full domain theory of ethics; it only encodes the identity and step-comparison structure required by the forcing chain.
proof idea
The proof is a one-line wrapper that applies the simp tactic to the definition of ethicsCost, which immediately yields zero from the equality case.
why it matters
This theorem supports the downstream definition of ethicsRealization, which constructs a LogicRealization with Carrier equal to MoralImprovementStep, Cost equal to Nat, and compare equal to ethicsCost. It thereby supplies the zero-cost identity axiom needed for the ethical domain to integrate with the broader forcing chain.
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