pow_tail_strict_of_square

Exact expanded PA statement

forall p e x s n. (exists bcf_le_gap_bpsts_base. bcf_le_gap_bpsts_base + (1) = p) -> (exists bcf_le_gap_bpsts_exponent. bcf_le_gap_bpsts_exponent + (2) = e) -> (exists bpvi_b_bpsts_square_power bpvi_c_bpsts_square_power. ((forall bpvi_i_bpsts_square_power. (exists bpvi_repeat_gap_bpsts_square_power. bpvi_repeat_gap_bpsts_square_power + S bpvi_i_bpsts_square_power = 2) -> (((exists bpvi_h_bpsts_square_power_repeat. bpvi_h_bpsts_square_power_repeat + S (p) = S ((S (bpvi_i_bpsts_square_power)) * bpvi_c_bpsts_square_power)) /\ exists bpvi_q_bpsts_square_power_repeat. bpvi_b_bpsts_square_power = bpvi_q_bpsts_square_power_repeat * S ((S (bpvi_i_bpsts_square_power)) * bpvi_c_bpsts_square_power) + (p)))) /\ (exists bpvi_u_bpsts_square_power bpvi_v_bpsts_square_power. ((((exists bpvi_h_bpsts_square_power_start. bpvi_h_bpsts_square_power_start + S (1) = S ((S (0)) * bpvi_v_bpsts_square_power)) /\ exists bpvi_q_bpsts_square_power_start. bpvi_u_bpsts_square_power = bpvi_q_bpsts_square_power_start * S ((S (0)) * bpvi_v_bpsts_square_power) + (1))) /\ ((((exists bpvi_h_bpsts_square_power_terminal. bpvi_h_bpsts_square_power_terminal + S (s) = S ((S (2)) * bpvi_v_bpsts_square_power)) /\ exists bpvi_q_bpsts_square_power_terminal. bpvi_u_bpsts_square_power = bpvi_q_bpsts_square_power_terminal * S ((S (2)) * bpvi_v_bpsts_square_power) + (s))) /\ forall bpvi_j_bpsts_square_power. (exists bpvi_product_gap_bpsts_square_power. bpvi_product_gap_bpsts_square_power + S bpvi_j_bpsts_square_power = 2) -> exists bpvi_factor_bpsts_square_power bpvi_partial_bpsts_square_power bpvi_successor_bpsts_square_power. ((((exists bpvi_h_bpsts_square_power_factor. bpvi_h_bpsts_square_power_factor + S (bpvi_factor_bpsts_square_power) = S ((S (bpvi_j_bpsts_square_power)) * bpvi_c_bpsts_square_power)) /\ exists bpvi_q_bpsts_square_power_factor. bpvi_b_bpsts_square_power = bpvi_q_bpsts_square_power_factor * S ((S (bpvi_j_bpsts_square_power)) * bpvi_c_bpsts_square_power) + (bpvi_factor_bpsts_square_power))) /\ ((((exists bpvi_h_bpsts_square_power_partial. bpvi_h_bpsts_square_power_partial + S (bpvi_partial_bpsts_square_power) = S ((S (bpvi_j_bpsts_square_power)) * bpvi_v_bpsts_square_power)) /\ exists bpvi_q_bpsts_square_power_partial. bpvi_u_bpsts_square_power = bpvi_q_bpsts_square_power_partial * S ((S (bpvi_j_bpsts_square_power)) * bpvi_v_bpsts_square_power) + (bpvi_partial_bpsts_square_power))) /\ ((((exists bpvi_h_bpsts_square_power_successor. bpvi_h_bpsts_square_power_successor + S (bpvi_successor_bpsts_square_power) = S ((S (S bpvi_j_bpsts_square_power)) * bpvi_v_bpsts_square_power)) /\ exists bpvi_q_bpsts_square_power_successor. bpvi_u_bpsts_square_power = bpvi_q_bpsts_square_power_successor * S ((S (S bpvi_j_bpsts_square_power)) * bpvi_v_bpsts_square_power) + (bpvi_successor_bpsts_square_power))) /\ bpvi_successor_bpsts_square_power = bpvi_partial_bpsts_square_power * bpvi_factor_bpsts_square_power)))))))) -> (exists ff_b_bpsts_tail_power ff_c_bpsts_tail_power. ((forall ff_i_bpsts_tail_power_repeat. (exists ff_lt_bpsts_tail_power_repeat_bound. ff_lt_bpsts_tail_power_repeat_bound + S ff_i_bpsts_tail_power_repeat = e) -> (((exists ff_h_bpsts_tail_power_repeat_decoded. ff_h_bpsts_tail_power_repeat_decoded + S (p) = S ((S (ff_i_bpsts_tail_power_repeat)) * ff_c_bpsts_tail_power)) /\ exists ff_q_bpsts_tail_power_repeat_decoded. ff_b_bpsts_tail_power = ff_q_bpsts_tail_power_repeat_decoded * S ((S (ff_i_bpsts_tail_power_repeat)) * ff_c_bpsts_tail_power) + (p)))) /\ (exists ff_u_bpsts_tail_power_product ff_v_bpsts_tail_power_product. ((((exists ff_h_bpsts_tail_power_product_start. ff_h_bpsts_tail_power_product_start + S (1) = S ((S (0)) * ff_v_bpsts_tail_power_product)) /\ exists ff_q_bpsts_tail_power_product_start. ff_u_bpsts_tail_power_product = ff_q_bpsts_tail_power_product_start * S ((S (0)) * ff_v_bpsts_tail_power_product) + (1))) /\ ((((exists ff_h_bpsts_tail_power_product_terminal. ff_h_bpsts_tail_power_product_terminal + S (x) = S ((S (e)) * ff_v_bpsts_tail_power_product)) /\ exists ff_q_bpsts_tail_power_product_terminal. ff_u_bpsts_tail_power_product = ff_q_bpsts_tail_power_product_terminal * S ((S (e)) * ff_v_bpsts_tail_power_product) + (x))) /\ forall ff_i_bpsts_tail_power_product. (exists ff_lt_bpsts_tail_power_product_bound. ff_lt_bpsts_tail_power_product_bound + S ff_i_bpsts_tail_power_product = e) -> exists ff_p_bpsts_tail_power_product ff_r_bpsts_tail_power_product ff_s_bpsts_tail_power_product. ((((exists ff_h_bpsts_tail_power_product_factor. ff_h_bpsts_tail_power_product_factor + S (ff_p_bpsts_tail_power_product) = S ((S (ff_i_bpsts_tail_power_product)) * ff_c_bpsts_tail_power)) /\ exists ff_q_bpsts_tail_power_product_factor. ff_b_bpsts_tail_power = ff_q_bpsts_tail_power_product_factor * S ((S (ff_i_bpsts_tail_power_product)) * ff_c_bpsts_tail_power) + (ff_p_bpsts_tail_power_product))) /\ ((((exists ff_h_bpsts_tail_power_product_partial. ff_h_bpsts_tail_power_product_partial + S (ff_r_bpsts_tail_power_product) = S ((S (ff_i_bpsts_tail_power_product)) * ff_v_bpsts_tail_power_product)) /\ exists ff_q_bpsts_tail_power_product_partial. ff_u_bpsts_tail_power_product = ff_q_bpsts_tail_power_product_partial * S ((S (ff_i_bpsts_tail_power_product)) * ff_v_bpsts_tail_power_product) + (ff_r_bpsts_tail_power_product))) /\ ((((exists ff_h_bpsts_tail_power_product_successor. ff_h_bpsts_tail_power_product_successor + S (ff_s_bpsts_tail_power_product) = S ((S (S ff_i_bpsts_tail_power_product)) * ff_v_bpsts_tail_power_product)) /\ exists ff_q_bpsts_tail_power_product_successor. ff_u_bpsts_tail_power_product = ff_q_bpsts_tail_power_product_successor * S ((S (S ff_i_bpsts_tail_power_product)) * ff_v_bpsts_tail_power_product) + (ff_s_bpsts_tail_power_product))) /\ ff_s_bpsts_tail_power_product = ff_r_bpsts_tail_power_product * ff_p_bpsts_tail_power_product)))))))) -> (exists bcf_lt_gap_bpsts_source. bcf_lt_gap_bpsts_source + S (n) = s) -> (exists bcf_lt_gap_bpsts_result. bcf_lt_gap_bpsts_result + S (n) = x)