ND0336 — PolynomialEquivalent(b,c,L,d,e,M)

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

∀ pfrep_power_working_euclidean_definition. ∀ pfrep_left_working_euclidean_definition. ∀ pfrep_right_working_euclidean_definition. PolynomialPowerCoefficient(b,c,L,pfrep_power_working_euclidean_definition,pfrep_left_working_euclidean_definition) → PolynomialPowerCoefficient(d,e,M,pfrep_power_working_euclidean_definition,pfrep_right_working_euclidean_definition) → pfrep_left_working_euclidean_definition = pfrep_right_working_euclidean_definition

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

Hygienic expanded first-order definition

forall pfrep_power_working_euclidean_definition pfrep_left_working_euclidean_definition pfrep_right_working_euclidean_definition. ((exists pfrep_position_working_euclidean_definitionfirst. ((pfrep_position_working_euclidean_definitionfirst+S (pfrep_power_working_euclidean_definition)=((L))) /\ ((((exists ff_h_pfp_working_euclidean_definitionfirstentry. ff_h_pfp_working_euclidean_definitionfirstentry + S (pfrep_left_working_euclidean_definition) = S ((S (pfrep_position_working_euclidean_definitionfirst)) * (c))) /\ exists ff_q_pfp_working_euclidean_definitionfirstentry. (b) = ff_q_pfp_working_euclidean_definitionfirstentry * S ((S (pfrep_position_working_euclidean_definitionfirst)) * (c)) + (pfrep_left_working_euclidean_definition)))))) \/ (((exists pfrep_gap_working_euclidean_definitionfirstoutside. pfrep_gap_working_euclidean_definitionfirstoutside+((L))=(pfrep_power_working_euclidean_definition)) /\ (((pfrep_left_working_euclidean_definition)=0))))) -> ((exists pfrep_position_working_euclidean_definitionsecond. ((pfrep_position_working_euclidean_definitionsecond+S (pfrep_power_working_euclidean_definition)=((M))) /\ ((((exists ff_h_pfp_working_euclidean_definitionsecondentry. ff_h_pfp_working_euclidean_definitionsecondentry + S (pfrep_right_working_euclidean_definition) = S ((S (pfrep_position_working_euclidean_definitionsecond)) * (e))) /\ exists ff_q_pfp_working_euclidean_definitionsecondentry. (d) = ff_q_pfp_working_euclidean_definitionsecondentry * S ((S (pfrep_position_working_euclidean_definitionsecond)) * (e)) + (pfrep_right_working_euclidean_definition)))))) \/ (((exists pfrep_gap_working_euclidean_definitionsecondoutside. pfrep_gap_working_euclidean_definitionsecondoutside+((M))=(pfrep_power_working_euclidean_definition)) /\ (((pfrep_right_working_euclidean_definition)=0))))) -> pfrep_left_working_euclidean_definition=pfrep_right_working_euclidean_definition

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

Direct definition dependencies

PolynomialPowerCoefficient(b,c,L,k,a)

Definitions depending on this notation

FpPolynomialRightDivides(p,db,dc,D,ab,ac,L)CommonRepresentatives(ab,ac,L,bb,bc,M,ub,uc,vb,vc,K)FpPolynomialAlignedAdd(p,ab,ac,L,bb,bc,M,rb,rc,N)

Checked theorems using this definition