ND0155

SignedFloor(p,n,m,q,t,r)

The genuine signed floor equation (p−n)=m·(q−t)+r and strict natural remainder bound r<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. Exact original first-admission records.

Definition in prerequisite notation

p + m · t = n + m · q + r ∧ Lt(r,m)

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

Hygienic expanded first-order definition
((p) + (m) * (t) = ((n) + (m) * (q)) + (r) /\ exists sif_gap_lowerlayer. sif_gap_lowerlayer + S (r) = (m))

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

none

Checked theorems using this definition