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
∀ ff_i_defined_repeat. Lt(ff_i_defined_repeat,l) → BetaAt(b,c,ff_i_defined_repeat,a)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall ff_i_defined_repeat. (exists ff_lt_defined_repeat_bound. ff_lt_defined_repeat_bound + S ff_i_defined_repeat = l) -> (((exists ff_h_defined_repeat_decoded. ff_h_defined_repeat_decoded + S (a) = S ((S (ff_i_defined_repeat)) * c)) /\ exists ff_q_defined_repeat_decoded. b = ff_q_defined_repeat_decoded * S ((S (ff_i_defined_repeat)) * c) + (a)))The 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
PX0014 · prime_field_polynomial_left_pad_existsPX0018 · prime_field_polynomial_zero_suffix_left_padPX0021 · prime_field_polynomial_zero_power_coefficientPX0022 · prime_field_polynomial_zero_prefix_equivalent_emptyPX0031 · prime_field_polynomial_quotient_prefix_remainder_zeroPX0034 · prime_field_polynomial_trim_zero_prefix_cut_boundPX0035 · prime_field_polynomial_trim_zero_prefix_remainder_boundPX003E · prime_field_convolution_prefix_empty_left_zeroPX003F · prime_field_polynomial_division_coefficient_identityPX005D · polynomial_left_pad_zero_prefixPX0068 · prime_field_convolution_coefficient_before_left_padding_leftPX0069 · prime_field_convolution_coefficient_before_left_padding_rightPX006E · prime_field_polynomial_convolution_left_padding_equivalent_leftPX006F · prime_field_polynomial_convolution_left_padding_equivalent_right