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
PC0005 · polynomial_zero_extended_zero_valuePC000A · polynomial_diagonal_term_zero_leftPC000B · polynomial_diagonal_term_zero_rightPC0018 · prime_field_convolution_coefficient_zero_leftPC0019 · prime_field_convolution_coefficient_zero_rightPC001A · prime_field_convolution_coefficient_zero_past_supportPC002B · prime_field_polynomial_convolution_zero_leftPC002C · prime_field_polynomial_convolution_zero_rightPC0031 · prime_field_polynomial_represented_degree_excludes_zeroPC0032 · prime_field_polynomial_monic_degree_examples