PD0031 · conservative definition

BalancedInverse

a times b is congruent to one modulo m.

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

BalancedInverse(m, a, b)

Exact expansion

exists dp_u dp_v. (a) * (b) + m * dp_u = 1 + m * dp_v

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

Used by conservative definitions

none

All transitive conservative prerequisites

Used by theorem statements or local proof propositions

Grand-campaign planning vocabulary

Locate BalancedInverse in the global campaign vocabulary →

Reviewed BalancedInverse corresponds to blueprint BalancedInverse 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.