PD0007

DivRem(n,d,q,r)

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.

q and r are a quotient and a strict remainder for n by d.

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

Definition in prerequisite notation

n = d · q + r ∧ Lt(r,d)

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

Hygienic expanded first-order definition 
n = d * q + r /\ exists h. h + S r = d

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

Direct definition dependencies

Lt(a,b)

Definitions depending on this notation

DivisionPrefix(m,b,c,qb,qc,rb,rc,l)

Checked theorems using this definition

PP0001 · prime_field_polynomial_normalization_from_division