PD0031

BalancedInverse(m,a,b)

a times b is congruent to one modulo m.

Conservative notation; not a theorem, primitive, or axiom.

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

Definition in prerequisite notation

ModEq(m,a · b,1)

Only definitions earlier in this acyclic notation graph are used here.

Hygienic expanded first-order definition
exists dp_u dp_v. (a) * (b) + m * dp_u = 1 + m * dp_v

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.

Direct definition dependencies

Definitions depending on this notation

Checked theorems using this definition

none directly; see definition consumers