ND0061

SignedAlternatingCofactorTerm(ap,an,bp,bn,i,p,n)

The exact positive/negative natural-pair product with signs exchanged precisely at odd cofactor positions.

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 ff_even_mce_term_breakthrough. i = 2 * ff_even_mce_term_breakthrough) /\ (p = (ap) * (bp) + (an) * (bn) /\ n = (ap) * (bn) + (an) * (bp))) \/ ((exists ff_odd_mce_term_breakthrough. i = 2 * ff_odd_mce_term_breakthrough + 1) /\ (p = (ap) * (bn) + (an) * (bp) /\ n = (ap) * (bp) + (an) * (bn)))

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

Direct definition dependencies

Even(n)Odd(n)

Definitions depending on this notation

SignedAlternatingProductPrefix(ab,ac,db,dc,eb,ec,fb,fc,ub,uc,vb,vc,l)

Checked theorems using this definition

CE000C · signed_alternating_cofactor_term_existsCE000D · signed_alternating_cofactor_term_functionalCE000E · signed_alternating_cofactor_term_evenCE000F · signed_alternating_cofactor_term_oddCE0010 · signed_alternating_cofactor_term_exists_uniqueCE0012 · signed_alternating_product_prefix_extendCE0015 · signed_alternating_product_prefix_exact_term

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