power_quotient_prefix_decoded_divrem

Exact expanded PA statement

forall p n b c l i q. (forall bls_index_legendre_successor_projection. (exists bls_gap_legendre_successor_projection_bound. bls_gap_legendre_successor_projection_bound + S (bls_index_legendre_successor_projection) = (l)) -> exists bls_power_legendre_successor_projection bls_quotient_legendre_successor_projection bls_remainder_legendre_successor_projection. ((exists bpvi_b_bls_legendre_successor_projection_power bpvi_c_bls_legendre_successor_projection_power. ((forall bpvi_i_bls_legendre_successor_projection_power. (exists bpvi_repeat_gap_bls_legendre_successor_projection_power. bpvi_repeat_gap_bls_legendre_successor_projection_power + S bpvi_i_bls_legendre_successor_projection_power = S bls_index_legendre_successor_projection) -> (((exists bpvi_h_bls_legendre_successor_projection_power_repeat. bpvi_h_bls_legendre_successor_projection_power_repeat + S (p) = S ((S (bpvi_i_bls_legendre_successor_projection_power)) * bpvi_c_bls_legendre_successor_projection_power)) /\ exists bpvi_q_bls_legendre_successor_projection_power_repeat. bpvi_b_bls_legendre_successor_projection_power = bpvi_q_bls_legendre_successor_projection_power_repeat * S ((S (bpvi_i_bls_legendre_successor_projection_power)) * bpvi_c_bls_legendre_successor_projection_power) + (p)))) /\ (exists bpvi_u_bls_legendre_successor_projection_power bpvi_v_bls_legendre_successor_projection_power. ((((exists bpvi_h_bls_legendre_successor_projection_power_start. bpvi_h_bls_legendre_successor_projection_power_start + S (1) = S ((S (0)) * bpvi_v_bls_legendre_successor_projection_power)) /\ exists bpvi_q_bls_legendre_successor_projection_power_start. bpvi_u_bls_legendre_successor_projection_power = bpvi_q_bls_legendre_successor_projection_power_start * S ((S (0)) * bpvi_v_bls_legendre_successor_projection_power) + (1))) /\ ((((exists bpvi_h_bls_legendre_successor_projection_power_terminal. bpvi_h_bls_legendre_successor_projection_power_terminal + S (bls_power_legendre_successor_projection) = S ((S (S bls_index_legendre_successor_projection)) * bpvi_v_bls_legendre_successor_projection_power)) /\ exists bpvi_q_bls_legendre_successor_projection_power_terminal. bpvi_u_bls_legendre_successor_projection_power = bpvi_q_bls_legendre_successor_projection_power_terminal * S ((S (S bls_index_legendre_successor_projection)) * bpvi_v_bls_legendre_successor_projection_power) + (bls_power_legendre_successor_projection))) /\ forall bpvi_j_bls_legendre_successor_projection_power. (exists bpvi_product_gap_bls_legendre_successor_projection_power. bpvi_product_gap_bls_legendre_successor_projection_power + S bpvi_j_bls_legendre_successor_projection_power = S bls_index_legendre_successor_projection) -> exists bpvi_factor_bls_legendre_successor_projection_power bpvi_partial_bls_legendre_successor_projection_power bpvi_successor_bls_legendre_successor_projection_power. ((((exists bpvi_h_bls_legendre_successor_projection_power_factor. bpvi_h_bls_legendre_successor_projection_power_factor + S (bpvi_factor_bls_legendre_successor_projection_power) = S ((S (bpvi_j_bls_legendre_successor_projection_power)) * bpvi_c_bls_legendre_successor_projection_power)) /\ exists bpvi_q_bls_legendre_successor_projection_power_factor. bpvi_b_bls_legendre_successor_projection_power = bpvi_q_bls_legendre_successor_projection_power_factor * S ((S (bpvi_j_bls_legendre_successor_projection_power)) * bpvi_c_bls_legendre_successor_projection_power) + (bpvi_factor_bls_legendre_successor_projection_power))) /\ ((((exists bpvi_h_bls_legendre_successor_projection_power_partial. bpvi_h_bls_legendre_successor_projection_power_partial + S (bpvi_partial_bls_legendre_successor_projection_power) = S ((S (bpvi_j_bls_legendre_successor_projection_power)) * bpvi_v_bls_legendre_successor_projection_power)) /\ exists bpvi_q_bls_legendre_successor_projection_power_partial. bpvi_u_bls_legendre_successor_projection_power = bpvi_q_bls_legendre_successor_projection_power_partial * S ((S (bpvi_j_bls_legendre_successor_projection_power)) * bpvi_v_bls_legendre_successor_projection_power) + (bpvi_partial_bls_legendre_successor_projection_power))) /\ ((((exists bpvi_h_bls_legendre_successor_projection_power_successor. bpvi_h_bls_legendre_successor_projection_power_successor + S (bpvi_successor_bls_legendre_successor_projection_power) = S ((S (S bpvi_j_bls_legendre_successor_projection_power)) * bpvi_v_bls_legendre_successor_projection_power)) /\ exists bpvi_q_bls_legendre_successor_projection_power_successor. bpvi_u_bls_legendre_successor_projection_power = bpvi_q_bls_legendre_successor_projection_power_successor * S ((S (S bpvi_j_bls_legendre_successor_projection_power)) * bpvi_v_bls_legendre_successor_projection_power) + (bpvi_successor_bls_legendre_successor_projection_power))) /\ bpvi_successor_bls_legendre_successor_projection_power = bpvi_partial_bls_legendre_successor_projection_power * bpvi_factor_bls_legendre_successor_projection_power)))))))) /\ ((((exists ff_h_bls_legendre_successor_projection_quotient_entry. ff_h_bls_legendre_successor_projection_quotient_entry + S (bls_quotient_legendre_successor_projection) = S ((S (bls_index_legendre_successor_projection)) * c)) /\ exists ff_q_bls_legendre_successor_projection_quotient_entry. b = ff_q_bls_legendre_successor_projection_quotient_entry * S ((S (bls_index_legendre_successor_projection)) * c) + (bls_quotient_legendre_successor_projection))) /\ ((n = bls_power_legendre_successor_projection * bls_quotient_legendre_successor_projection + bls_remainder_legendre_successor_projection /\ exists bls_remainder_gap_legendre_successor_projection_division. bls_remainder_gap_legendre_successor_projection_division + S (bls_remainder_legendre_successor_projection) = bls_power_legendre_successor_projection))))) -> (exists blsr_lt_gap_legendre_successor_projection_index. blsr_lt_gap_legendre_successor_projection_index + S (i) = (l)) -> (((exists ff_h_legendre_successor_projection_entry. ff_h_legendre_successor_projection_entry + S (q) = S ((S (i)) * c)) /\ exists ff_q_legendre_successor_projection_entry. b = ff_q_legendre_successor_projection_entry * S ((S (i)) * c) + (q))) -> exists D r. ((exists bpvi_b_legendre_successor_projection_power bpvi_c_legendre_successor_projection_power. ((forall bpvi_i_legendre_successor_projection_power. (exists bpvi_repeat_gap_legendre_successor_projection_power. bpvi_repeat_gap_legendre_successor_projection_power + S bpvi_i_legendre_successor_projection_power = S i) -> (((exists bpvi_h_legendre_successor_projection_power_repeat. bpvi_h_legendre_successor_projection_power_repeat + S (p) = S ((S (bpvi_i_legendre_successor_projection_power)) * bpvi_c_legendre_successor_projection_power)) /\ exists bpvi_q_legendre_successor_projection_power_repeat. bpvi_b_legendre_successor_projection_power = bpvi_q_legendre_successor_projection_power_repeat * S ((S (bpvi_i_legendre_successor_projection_power)) * bpvi_c_legendre_successor_projection_power) + (p)))) /\ (exists bpvi_u_legendre_successor_projection_power bpvi_v_legendre_successor_projection_power. ((((exists bpvi_h_legendre_successor_projection_power_start. bpvi_h_legendre_successor_projection_power_start + S (1) = S ((S (0)) * bpvi_v_legendre_successor_projection_power)) /\ exists bpvi_q_legendre_successor_projection_power_start. bpvi_u_legendre_successor_projection_power = bpvi_q_legendre_successor_projection_power_start * S ((S (0)) * bpvi_v_legendre_successor_projection_power) + (1))) /\ ((((exists bpvi_h_legendre_successor_projection_power_terminal. bpvi_h_legendre_successor_projection_power_terminal + S (D) = S ((S (S i)) * bpvi_v_legendre_successor_projection_power)) /\ exists bpvi_q_legendre_successor_projection_power_terminal. bpvi_u_legendre_successor_projection_power = bpvi_q_legendre_successor_projection_power_terminal * S ((S (S i)) * bpvi_v_legendre_successor_projection_power) + (D))) /\ forall bpvi_j_legendre_successor_projection_power. (exists bpvi_product_gap_legendre_successor_projection_power. bpvi_product_gap_legendre_successor_projection_power + S bpvi_j_legendre_successor_projection_power = S i) -> exists bpvi_factor_legendre_successor_projection_power bpvi_partial_legendre_successor_projection_power bpvi_successor_legendre_successor_projection_power. ((((exists bpvi_h_legendre_successor_projection_power_factor. bpvi_h_legendre_successor_projection_power_factor + S (bpvi_factor_legendre_successor_projection_power) = S ((S (bpvi_j_legendre_successor_projection_power)) * bpvi_c_legendre_successor_projection_power)) /\ exists bpvi_q_legendre_successor_projection_power_factor. bpvi_b_legendre_successor_projection_power = bpvi_q_legendre_successor_projection_power_factor * S ((S (bpvi_j_legendre_successor_projection_power)) * bpvi_c_legendre_successor_projection_power) + (bpvi_factor_legendre_successor_projection_power))) /\ ((((exists bpvi_h_legendre_successor_projection_power_partial. bpvi_h_legendre_successor_projection_power_partial + S (bpvi_partial_legendre_successor_projection_power) = S ((S (bpvi_j_legendre_successor_projection_power)) * bpvi_v_legendre_successor_projection_power)) /\ exists bpvi_q_legendre_successor_projection_power_partial. bpvi_u_legendre_successor_projection_power = bpvi_q_legendre_successor_projection_power_partial * S ((S (bpvi_j_legendre_successor_projection_power)) * bpvi_v_legendre_successor_projection_power) + (bpvi_partial_legendre_successor_projection_power))) /\ ((((exists bpvi_h_legendre_successor_projection_power_successor. bpvi_h_legendre_successor_projection_power_successor + S (bpvi_successor_legendre_successor_projection_power) = S ((S (S bpvi_j_legendre_successor_projection_power)) * bpvi_v_legendre_successor_projection_power)) /\ exists bpvi_q_legendre_successor_projection_power_successor. bpvi_u_legendre_successor_projection_power = bpvi_q_legendre_successor_projection_power_successor * S ((S (S bpvi_j_legendre_successor_projection_power)) * bpvi_v_legendre_successor_projection_power) + (bpvi_successor_legendre_successor_projection_power))) /\ bpvi_successor_legendre_successor_projection_power = bpvi_partial_legendre_successor_projection_power * bpvi_factor_legendre_successor_projection_power)))))))) /\ (((n) = (D) * (q) + (r) /\ exists blsr_lt_gap_legendre_successor_projection_division_bound. blsr_lt_gap_legendre_successor_projection_division_bound + S (r) = (D))))