power_quotient_prefix_tail_entry_zero

Exact expanded PA statement

forall p n b c l i. ((~(p = 1) /\ forall frm_prime_left_b5cvptez_prime frm_prime_right_b5cvptez_prime. p = frm_prime_left_b5cvptez_prime * frm_prime_right_b5cvptez_prime -> frm_prime_left_b5cvptez_prime = 1 \/ frm_prime_right_b5cvptez_prime = 1)) -> (forall bls_index_b5cvptez_prefix. (exists bls_gap_b5cvptez_prefix_bound. bls_gap_b5cvptez_prefix_bound + S (bls_index_b5cvptez_prefix) = (l)) -> exists bls_power_b5cvptez_prefix bls_quotient_b5cvptez_prefix bls_remainder_b5cvptez_prefix. ((exists bpvi_b_bls_b5cvptez_prefix_power bpvi_c_bls_b5cvptez_prefix_power. ((forall bpvi_i_bls_b5cvptez_prefix_power. (exists bpvi_repeat_gap_bls_b5cvptez_prefix_power. bpvi_repeat_gap_bls_b5cvptez_prefix_power + S bpvi_i_bls_b5cvptez_prefix_power = S bls_index_b5cvptez_prefix) -> (((exists bpvi_h_bls_b5cvptez_prefix_power_repeat. bpvi_h_bls_b5cvptez_prefix_power_repeat + S (p) = S ((S (bpvi_i_bls_b5cvptez_prefix_power)) * bpvi_c_bls_b5cvptez_prefix_power)) /\ exists bpvi_q_bls_b5cvptez_prefix_power_repeat. bpvi_b_bls_b5cvptez_prefix_power = bpvi_q_bls_b5cvptez_prefix_power_repeat * S ((S (bpvi_i_bls_b5cvptez_prefix_power)) * bpvi_c_bls_b5cvptez_prefix_power) + (p)))) /\ (exists bpvi_u_bls_b5cvptez_prefix_power bpvi_v_bls_b5cvptez_prefix_power. ((((exists bpvi_h_bls_b5cvptez_prefix_power_start. bpvi_h_bls_b5cvptez_prefix_power_start + S (1) = S ((S (0)) * bpvi_v_bls_b5cvptez_prefix_power)) /\ exists bpvi_q_bls_b5cvptez_prefix_power_start. bpvi_u_bls_b5cvptez_prefix_power = bpvi_q_bls_b5cvptez_prefix_power_start * S ((S (0)) * bpvi_v_bls_b5cvptez_prefix_power) + (1))) /\ ((((exists bpvi_h_bls_b5cvptez_prefix_power_terminal. bpvi_h_bls_b5cvptez_prefix_power_terminal + S (bls_power_b5cvptez_prefix) = S ((S (S bls_index_b5cvptez_prefix)) * bpvi_v_bls_b5cvptez_prefix_power)) /\ exists bpvi_q_bls_b5cvptez_prefix_power_terminal. bpvi_u_bls_b5cvptez_prefix_power = bpvi_q_bls_b5cvptez_prefix_power_terminal * S ((S (S bls_index_b5cvptez_prefix)) * bpvi_v_bls_b5cvptez_prefix_power) + (bls_power_b5cvptez_prefix))) /\ forall bpvi_j_bls_b5cvptez_prefix_power. (exists bpvi_product_gap_bls_b5cvptez_prefix_power. bpvi_product_gap_bls_b5cvptez_prefix_power + S bpvi_j_bls_b5cvptez_prefix_power = S bls_index_b5cvptez_prefix) -> exists bpvi_factor_bls_b5cvptez_prefix_power bpvi_partial_bls_b5cvptez_prefix_power bpvi_successor_bls_b5cvptez_prefix_power. ((((exists bpvi_h_bls_b5cvptez_prefix_power_factor. bpvi_h_bls_b5cvptez_prefix_power_factor + S (bpvi_factor_bls_b5cvptez_prefix_power) = S ((S (bpvi_j_bls_b5cvptez_prefix_power)) * bpvi_c_bls_b5cvptez_prefix_power)) /\ exists bpvi_q_bls_b5cvptez_prefix_power_factor. bpvi_b_bls_b5cvptez_prefix_power = bpvi_q_bls_b5cvptez_prefix_power_factor * S ((S (bpvi_j_bls_b5cvptez_prefix_power)) * bpvi_c_bls_b5cvptez_prefix_power) + (bpvi_factor_bls_b5cvptez_prefix_power))) /\ ((((exists bpvi_h_bls_b5cvptez_prefix_power_partial. bpvi_h_bls_b5cvptez_prefix_power_partial + S (bpvi_partial_bls_b5cvptez_prefix_power) = S ((S (bpvi_j_bls_b5cvptez_prefix_power)) * bpvi_v_bls_b5cvptez_prefix_power)) /\ exists bpvi_q_bls_b5cvptez_prefix_power_partial. bpvi_u_bls_b5cvptez_prefix_power = bpvi_q_bls_b5cvptez_prefix_power_partial * S ((S (bpvi_j_bls_b5cvptez_prefix_power)) * bpvi_v_bls_b5cvptez_prefix_power) + (bpvi_partial_bls_b5cvptez_prefix_power))) /\ ((((exists bpvi_h_bls_b5cvptez_prefix_power_successor. bpvi_h_bls_b5cvptez_prefix_power_successor + S (bpvi_successor_bls_b5cvptez_prefix_power) = S ((S (S bpvi_j_bls_b5cvptez_prefix_power)) * bpvi_v_bls_b5cvptez_prefix_power)) /\ exists bpvi_q_bls_b5cvptez_prefix_power_successor. bpvi_u_bls_b5cvptez_prefix_power = bpvi_q_bls_b5cvptez_prefix_power_successor * S ((S (S bpvi_j_bls_b5cvptez_prefix_power)) * bpvi_v_bls_b5cvptez_prefix_power) + (bpvi_successor_bls_b5cvptez_prefix_power))) /\ bpvi_successor_bls_b5cvptez_prefix_power = bpvi_partial_bls_b5cvptez_prefix_power * bpvi_factor_bls_b5cvptez_prefix_power)))))))) /\ ((((exists ff_h_bls_b5cvptez_prefix_quotient_entry. ff_h_bls_b5cvptez_prefix_quotient_entry + S (bls_quotient_b5cvptez_prefix) = S ((S (bls_index_b5cvptez_prefix)) * c)) /\ exists ff_q_bls_b5cvptez_prefix_quotient_entry. b = ff_q_bls_b5cvptez_prefix_quotient_entry * S ((S (bls_index_b5cvptez_prefix)) * c) + (bls_quotient_b5cvptez_prefix))) /\ ((n = bls_power_b5cvptez_prefix * bls_quotient_b5cvptez_prefix + bls_remainder_b5cvptez_prefix /\ exists bls_remainder_gap_b5cvptez_prefix_division. bls_remainder_gap_b5cvptez_prefix_division + S (bls_remainder_b5cvptez_prefix) = bls_power_b5cvptez_prefix))))) -> (exists bcf_le_gap_b5cvptez_start. bcf_le_gap_b5cvptez_start + (n) = i) -> (exists bcf_lt_gap_b5cvptez_bound. bcf_lt_gap_b5cvptez_bound + S (i) = l) -> (((exists fs_h_b5cvptez_result. fs_h_b5cvptez_result + S (0) = S ((S (i)) * c)) /\ exists fs_q_b5cvptez_result. b = fs_q_b5cvptez_result * S ((S (i)) * c) + (0)))