BinaryModularPower(a,e,m,r)

Hygienic expanded first-order definition

exists ff_power_binary_advanced. ((exists ff_b_binary_advanced_value ff_c_binary_advanced_value. ((forall ff_i_binary_advanced_value_repeat. (exists ff_lt_binary_advanced_value_repeat_bound. ff_lt_binary_advanced_value_repeat_bound + S ff_i_binary_advanced_value_repeat = e) -> (((exists ff_h_binary_advanced_value_repeat_decoded. ff_h_binary_advanced_value_repeat_decoded + S (a) = S ((S (ff_i_binary_advanced_value_repeat)) * ff_c_binary_advanced_value)) /\ exists ff_q_binary_advanced_value_repeat_decoded. ff_b_binary_advanced_value = ff_q_binary_advanced_value_repeat_decoded * S ((S (ff_i_binary_advanced_value_repeat)) * ff_c_binary_advanced_value) + (a)))) /\ (exists ff_u_binary_advanced_value_product ff_v_binary_advanced_value_product. ((((exists ff_h_binary_advanced_value_product_start. ff_h_binary_advanced_value_product_start + S (1) = S ((S (0)) * ff_v_binary_advanced_value_product)) /\ exists ff_q_binary_advanced_value_product_start. ff_u_binary_advanced_value_product = ff_q_binary_advanced_value_product_start * S ((S (0)) * ff_v_binary_advanced_value_product) + (1))) /\ ((((exists ff_h_binary_advanced_value_product_terminal. ff_h_binary_advanced_value_product_terminal + S (ff_power_binary_advanced) = S ((S (e)) * ff_v_binary_advanced_value_product)) /\ exists ff_q_binary_advanced_value_product_terminal. ff_u_binary_advanced_value_product = ff_q_binary_advanced_value_product_terminal * S ((S (e)) * ff_v_binary_advanced_value_product) + (ff_power_binary_advanced))) /\ forall ff_i_binary_advanced_value_product. (exists ff_lt_binary_advanced_value_product_bound. ff_lt_binary_advanced_value_product_bound + S ff_i_binary_advanced_value_product = e) -> exists ff_p_binary_advanced_value_product ff_r_binary_advanced_value_product ff_s_binary_advanced_value_product. ((((exists ff_h_binary_advanced_value_product_factor. ff_h_binary_advanced_value_product_factor + S (ff_p_binary_advanced_value_product) = S ((S (ff_i_binary_advanced_value_product)) * ff_c_binary_advanced_value)) /\ exists ff_q_binary_advanced_value_product_factor. ff_b_binary_advanced_value = ff_q_binary_advanced_value_product_factor * S ((S (ff_i_binary_advanced_value_product)) * ff_c_binary_advanced_value) + (ff_p_binary_advanced_value_product))) /\ ((((exists ff_h_binary_advanced_value_product_partial. ff_h_binary_advanced_value_product_partial + S (ff_r_binary_advanced_value_product) = S ((S (ff_i_binary_advanced_value_product)) * ff_v_binary_advanced_value_product)) /\ exists ff_q_binary_advanced_value_product_partial. ff_u_binary_advanced_value_product = ff_q_binary_advanced_value_product_partial * S ((S (ff_i_binary_advanced_value_product)) * ff_v_binary_advanced_value_product) + (ff_r_binary_advanced_value_product))) /\ ((((exists ff_h_binary_advanced_value_product_successor. ff_h_binary_advanced_value_product_successor + S (ff_s_binary_advanced_value_product) = S ((S (S ff_i_binary_advanced_value_product)) * ff_v_binary_advanced_value_product)) /\ exists ff_q_binary_advanced_value_product_successor. ff_u_binary_advanced_value_product = ff_q_binary_advanced_value_product_successor * S ((S (S ff_i_binary_advanced_value_product)) * ff_v_binary_advanced_value_product) + (ff_s_binary_advanced_value_product))) /\ ff_s_binary_advanced_value_product = ff_r_binary_advanced_value_product * ff_p_binary_advanced_value_product)))))))) /\ (((exists ff_gap_binary_advanced_residue. ff_gap_binary_advanced_residue + S (r) = m) /\ (exists ff_left_binary_advanced_residue_congruence ff_right_binary_advanced_residue_congruence. (ff_power_binary_advanced) + m * ff_left_binary_advanced_residue_congruence = (r) + m * ff_right_binary_advanced_residue_congruence))))

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