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_definitionOnly 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_definitionThe 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
PX000D · prime_field_polynomial_power_coefficient_functionalPX000F · prime_field_polynomial_equivalent_symmetricPX0010 · prime_field_polynomial_equivalent_transitivePX0011 · prime_field_polynomial_equal_implies_equivalentPX0012 · prime_field_polynomial_equivalent_implies_equal_same_lengthPX001B · prime_field_polynomial_left_pad_equivalentPX001C · prime_field_polynomial_trim_equivalentPX0022 · prime_field_polynomial_zero_prefix_equivalent_emptyPX006E · prime_field_polynomial_convolution_left_padding_equivalent_leftPX006F · prime_field_polynomial_convolution_left_padding_equivalent_rightPX0070 · prime_field_polynomial_convolution_both_left_paddings_equivalentPX0071 · prime_field_polynomial_convolution_both_left_paddings_existsPX0072 · prime_field_polynomial_equivalent_implies_left_padPX0075 · prime_field_polynomial_add_equivalent_congruentPX0076 · prime_field_polynomial_subtract_equivalent_congruentPX0077 · prime_field_polynomial_convolution_equivalent_congruent_leftPX0078 · prime_field_polynomial_convolution_equivalent_congruent_rightPX0079 · prime_field_polynomial_convolution_equivalent_congruent