PD0031

BalancedInverse(m,a,b)

Public research checkpoint, not admitted to Alpha or Stable. Alpha v30 remains 3222 checked-use theorems; Stable remains 432. The on-demand Alpha Lean service does not yet expose these checkpoint theorems; their independently checked literal bundles and unchanged sources are available below.

a times b is congruent to one modulo m.

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

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

BoundedNonzeroInverse(m,a)

Checked theorems using this definition

none directly; see definition consumers