ND0262 — BetaPrefixInto(b,c,l,B)

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

∀ fom_index_pfp_lowertier. Lt(fom_index_pfp_lowertier,l) → ∃ x. BetaAt(b,c,fom_index_pfp_lowertier,x) ∧ Lt(x,B)

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

Hygienic expanded first-order definition

forall fom_index_pfp_lowertier. (exists fom_gap_pfp_lowertier_index_bound. fom_gap_pfp_lowertier_index_bound + S (fom_index_pfp_lowertier) = (l)) -> exists fom_value_pfp_lowertier. ((((exists fom_beta_height_pfp_lowertier_entry. fom_beta_height_pfp_lowertier_entry + S (fom_value_pfp_lowertier) = S ((S (fom_index_pfp_lowertier)) * (c))) /\ exists fom_beta_quotient_pfp_lowertier_entry. (b) = fom_beta_quotient_pfp_lowertier_entry * S ((S (fom_index_pfp_lowertier)) * (c)) + (fom_value_pfp_lowertier))) /\ (exists fom_gap_pfp_lowertier_value_bound. fom_gap_pfp_lowertier_value_bound + S (fom_value_pfp_lowertier) = (B)))

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)BetaAt(b,c,i,x)

Definitions depending on this notation

FpPolyProduct(p,ab,ac,L,bb,bc,M,cb,cc,N)FpRepresentedDegree(p,b,c,L,d)FpPolynomialTrim(p,b,c,L,t,d,e,M)FpPolynomialDivisionExecution(p,ab,ac,L,bb,bc,d,qb,qc,q,rb,rc,R)

Checked theorems using this definition