primitiveOrderList_nodup
The lemma establishes that the canonical list of primitive virtues contains no duplicate entries. Researchers formalizing normal forms for micro-move coefficient tables in the DREAM scaffolding would cite this result to guarantee unique ordering in summation operations. The proof is a one-line wrapper that unfolds the list definition and invokes a decision procedure to confirm the absence of duplicates.
claimThe canonical list of primitive virtues $[Love, Justice, Forgiveness, Wisdom, Courage, Temperance, Prudence, Compassion, Gratitude, Patience, Humility, Hope, Creativity, Sacrifice]$ contains no repeated elements.
background
In the module on Micro-Move Normal Forms, which supplies canonical normal forms for micro-move coefficient tables supporting DREAM scaffolding, the primitive list is fixed as the explicit sequence of 14 virtues given above. This sequence serves as the reference order for indexing coefficients and moves in normal forms. The upstream definition supplies this concrete enumeration, which the lemma verifies satisfies the nodup property.
proof idea
The proof unfolds the definition of the canonical primitive list and applies the decide tactic to verify the nodup property directly from the concrete list.
why it matters in Recognition Science
This result feeds into the auxiliary theorem on aggregation of coefficients over row moves, which performs summation over filtered moves by relying on the unique ordering to ensure each primitive appears at most once. It supports the canonical normal form construction in the ethics module, aligning with the Recognition Science emphasis on unique representations.
scope and limits
- Does not establish any ordering properties beyond the absence of duplicates.
- Does not prove that this list is the only possible canonical order.
- Does not address coefficient summation or move aggregation directly.
formal statement (Lean)
34lemma primitiveOrderList_nodup : primitiveOrderList.Nodup := by
proof body
Term-mode proof.
35 unfold primitiveOrderList
36 decide
37
38/-- Micro moves: (pair scope, primitive, coefficient). -/