ND0003

MatrixAt(b,c,w,i,j,z)

The exact natural matrix entry stored at flattened beta index i*w+j.

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.

Hygienic expanded first-order definition

((exists fs_h_matrix_explorer. fs_h_matrix_explorer + S (z) = S ((S (i * w + j)) * c)) /\ exists fs_q_matrix_explorer. b = fs_q_matrix_explorer * S ((S (i * w + j)) * c) + (z))

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

none directly; see definition consumers

Separate complete second-wave branches: Full T13 proof · Alpha v27.