PowerDivides(p,e,n)

Hygienic expanded first-order definition

exists bpv_result_bertrand_defined_power_divides. ((exists ff_b_bertrand_defined_power_divides_power ff_c_bertrand_defined_power_divides_power. ((forall ff_i_bertrand_defined_power_divides_power_repeat. (exists ff_lt_bertrand_defined_power_divides_power_repeat_bound. ff_lt_bertrand_defined_power_divides_power_repeat_bound + S ff_i_bertrand_defined_power_divides_power_repeat = e) -> (((exists ff_h_bertrand_defined_power_divides_power_repeat_decoded. ff_h_bertrand_defined_power_divides_power_repeat_decoded + S (p) = S ((S (ff_i_bertrand_defined_power_divides_power_repeat)) * ff_c_bertrand_defined_power_divides_power)) /\ exists ff_q_bertrand_defined_power_divides_power_repeat_decoded. ff_b_bertrand_defined_power_divides_power = ff_q_bertrand_defined_power_divides_power_repeat_decoded * S ((S (ff_i_bertrand_defined_power_divides_power_repeat)) * ff_c_bertrand_defined_power_divides_power) + (p)))) /\ (exists ff_u_bertrand_defined_power_divides_power_product ff_v_bertrand_defined_power_divides_power_product. ((((exists ff_h_bertrand_defined_power_divides_power_product_start. ff_h_bertrand_defined_power_divides_power_product_start + S (1) = S ((S (0)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_start. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_start * S ((S (0)) * ff_v_bertrand_defined_power_divides_power_product) + (1))) /\ ((((exists ff_h_bertrand_defined_power_divides_power_product_terminal. ff_h_bertrand_defined_power_divides_power_product_terminal + S (bpv_result_bertrand_defined_power_divides) = S ((S (e)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_terminal. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_terminal * S ((S (e)) * ff_v_bertrand_defined_power_divides_power_product) + (bpv_result_bertrand_defined_power_divides))) /\ forall ff_i_bertrand_defined_power_divides_power_product. (exists ff_lt_bertrand_defined_power_divides_power_product_bound. ff_lt_bertrand_defined_power_divides_power_product_bound + S ff_i_bertrand_defined_power_divides_power_product = e) -> exists ff_p_bertrand_defined_power_divides_power_product ff_r_bertrand_defined_power_divides_power_product ff_s_bertrand_defined_power_divides_power_product. ((((exists ff_h_bertrand_defined_power_divides_power_product_factor. ff_h_bertrand_defined_power_divides_power_product_factor + S (ff_p_bertrand_defined_power_divides_power_product) = S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_c_bertrand_defined_power_divides_power)) /\ exists ff_q_bertrand_defined_power_divides_power_product_factor. ff_b_bertrand_defined_power_divides_power = ff_q_bertrand_defined_power_divides_power_product_factor * S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_c_bertrand_defined_power_divides_power) + (ff_p_bertrand_defined_power_divides_power_product))) /\ ((((exists ff_h_bertrand_defined_power_divides_power_product_partial. ff_h_bertrand_defined_power_divides_power_product_partial + S (ff_r_bertrand_defined_power_divides_power_product) = S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_partial. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_partial * S ((S (ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product) + (ff_r_bertrand_defined_power_divides_power_product))) /\ ((((exists ff_h_bertrand_defined_power_divides_power_product_successor. ff_h_bertrand_defined_power_divides_power_product_successor + S (ff_s_bertrand_defined_power_divides_power_product) = S ((S (S ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product)) /\ exists ff_q_bertrand_defined_power_divides_power_product_successor. ff_u_bertrand_defined_power_divides_power_product = ff_q_bertrand_defined_power_divides_power_product_successor * S ((S (S ff_i_bertrand_defined_power_divides_power_product)) * ff_v_bertrand_defined_power_divides_power_product) + (ff_s_bertrand_defined_power_divides_power_product))) /\ ff_s_bertrand_defined_power_divides_power_product = ff_r_bertrand_defined_power_divides_power_product * ff_p_bertrand_defined_power_divides_power_product)))))))) /\ (exists bpv_factor_bertrand_defined_power_divides_divides. n = bpv_result_bertrand_defined_power_divides * bpv_factor_bertrand_defined_power_divides_divides))

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