ND0296

PolynomialProductLength(L,M,N)

The proper product representation is empty if either input is empty; otherwise L+M=S N. This is a representation-length relation, not a claim that a possibly zero-leading polynomial has that degree.

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.

Definition in prerequisite notation

(L = 0 ∨ M = 0) ∧ N = 0 ∨ ¬L = 0 ∧ (¬M = 0 ∧ L + M = S N)

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

Hygienic expanded first-order definition 
(((((L))=0 \/ ((M))=0) /\ ((((N))=0)))) \/ (((~(((L))=0)) /\ (((~(((M))=0)) /\ ((((L))+((M))=S ((N))))))))

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

FpPolyProduct(p,ab,ac,L,bb,bc,M,cb,cc,N)

Checked theorems using this definition

PC0022 · polynomial_product_length_existsPC0023 · polynomial_product_length_functionalPC0028 · prime_field_polynomial_convolution_at_length_existsPC0029 · prime_field_polynomial_convolution_exists_uniquePC002E · polynomial_product_length_positive_inputsPC0034 · prime_field_polynomial_convolution_represented_degreePC0035 · prime_field_polynomial_convolution_represented_degree_exists