CF0004 · conservative definition

SignedBalance

A conservative signed-natural code balances the formal difference left−right.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Readable signature

SignedBalance(code, left, right)

Exact expansion

exists sb_pos_frontier sb_neg_frontier. (((code = 2 * sb_pos_frontier /\ sb_neg_frontier = 0) \/ exists sd_half_frontier. ((code = 2 * sd_half_frontier + 1 /\ sb_pos_frontier = 0) /\ sb_neg_frontier = S sd_half_frontier)) /\ left + sb_neg_frontier = right + sb_pos_frontier)

This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.

Definition neighborhood

Depends on conservative definitions

none

Used by conservative definitions

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All transitive conservative prerequisites

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Used by theorem statements or local proof propositions

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Grand-campaign planning vocabulary

Locate SignedBalance in the global campaign vocabulary →

Reviewed SignedBalance corresponds to blueprint SignedBalance with checked argument positions [0, 1, 2].

The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.