PD0008

ModEq(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.

Balanced-natural congruence modulo m.

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

Definition in prerequisite notation

∃ u. ∃ v. a + m · u = b + m · v

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

Hygienic expanded first-order definition 
exists u v. a + m * u = b + m * v

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

Direct definition dependencies

none — first-order arithmetic only

Definitions depending on this notation

CanonicalModularResidue(m,a,r)

Checked theorems using this definition

none directly; see definition consumers