Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
Definition in prerequisite notation
Pow(2,e,p)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists pa_b_bl_transport pa_c_bl_transport. ((forall pa_i_bl_transport_repeat. (exists pa_lt_bl_transport_repeat_bound. pa_lt_bl_transport_repeat_bound + S pa_i_bl_transport_repeat = e) -> (((exists pa_h_bl_transport_repeat_decoded. pa_h_bl_transport_repeat_decoded + S (2) = S ((S (pa_i_bl_transport_repeat)) * pa_c_bl_transport)) /\ exists pa_q_bl_transport_repeat_decoded. pa_b_bl_transport = pa_q_bl_transport_repeat_decoded * S ((S (pa_i_bl_transport_repeat)) * pa_c_bl_transport) + (2)))) /\ (exists pa_u_bl_transport_product pa_v_bl_transport_product. ((((exists pa_h_bl_transport_product_start. pa_h_bl_transport_product_start + S (1) = S ((S (0)) * pa_v_bl_transport_product)) /\ exists pa_q_bl_transport_product_start. pa_u_bl_transport_product = pa_q_bl_transport_product_start * S ((S (0)) * pa_v_bl_transport_product) + (1))) /\ ((((exists pa_h_bl_transport_product_terminal. pa_h_bl_transport_product_terminal + S (p) = S ((S (e)) * pa_v_bl_transport_product)) /\ exists pa_q_bl_transport_product_terminal. pa_u_bl_transport_product = pa_q_bl_transport_product_terminal * S ((S (e)) * pa_v_bl_transport_product) + (p))) /\ forall pa_i_bl_transport_product. (exists pa_lt_bl_transport_product_bound. pa_lt_bl_transport_product_bound + S pa_i_bl_transport_product = e) -> exists pa_p_bl_transport_product pa_r_bl_transport_product pa_s_bl_transport_product. ((((exists pa_h_bl_transport_product_factor. pa_h_bl_transport_product_factor + S (pa_p_bl_transport_product) = S ((S (pa_i_bl_transport_product)) * pa_c_bl_transport)) /\ exists pa_q_bl_transport_product_factor. pa_b_bl_transport = pa_q_bl_transport_product_factor * S ((S (pa_i_bl_transport_product)) * pa_c_bl_transport) + (pa_p_bl_transport_product))) /\ ((((exists pa_h_bl_transport_product_partial. pa_h_bl_transport_product_partial + S (pa_r_bl_transport_product) = S ((S (pa_i_bl_transport_product)) * pa_v_bl_transport_product)) /\ exists pa_q_bl_transport_product_partial. pa_u_bl_transport_product = pa_q_bl_transport_product_partial * S ((S (pa_i_bl_transport_product)) * pa_v_bl_transport_product) + (pa_r_bl_transport_product))) /\ ((((exists pa_h_bl_transport_product_successor. pa_h_bl_transport_product_successor + S (pa_s_bl_transport_product) = S ((S (S pa_i_bl_transport_product)) * pa_v_bl_transport_product)) /\ exists pa_q_bl_transport_product_successor. pa_u_bl_transport_product = pa_q_bl_transport_product_successor * S ((S (S pa_i_bl_transport_product)) * pa_v_bl_transport_product) + (pa_s_bl_transport_product))) /\ pa_s_bl_transport_product = pa_r_bl_transport_product * pa_p_bl_transport_product)))))))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
Checked theorems using this definition
PC0015 · binary_power_two_dominates_successorPC0016 · binary_power_two_order_reflects_exponentPC0017 · binary_power_two_strict_order_reflects_exponentPC0018 · pow_four_is_square_of_pow_twoPC0019 · central_binom_dominates_pow_twoPC0025 · binary_length_nonzero_componentsPC0026 · binary_half_scale_boundsPC0027 · pow_four_equals_binary_doublePC0028 · prime_cutoff_exponent_boundPC002A · prime_count_chebyshev_upperPC002E · central_binom_prime_count_exponent_bound