EuclideanLogarithmicExecution(a,b,ell,g,k)

Hygienic expanded first-order definition

(((((b) = 0 /\ (ell) = 1) \/ exists ff_exponent_bl_elb_milestone_length ff_lower_bl_elb_milestone_length ff_upper_bl_elb_milestone_length. (((ell) = S ff_exponent_bl_elb_milestone_length) /\ ((exists ff_positive_bl_elb_milestone_length. ff_positive_bl_elb_milestone_length + 1 = (b)) /\ ((exists pa_b_bl_elb_milestone_length_lower pa_c_bl_elb_milestone_length_lower. ((forall pa_i_bl_elb_milestone_length_lower_repeat. (exists pa_lt_bl_elb_milestone_length_lower_repeat_bound. pa_lt_bl_elb_milestone_length_lower_repeat_bound + S pa_i_bl_elb_milestone_length_lower_repeat = ff_exponent_bl_elb_milestone_length) -> (((exists pa_h_bl_elb_milestone_length_lower_repeat_decoded. pa_h_bl_elb_milestone_length_lower_repeat_decoded + S (2) = S ((S (pa_i_bl_elb_milestone_length_lower_repeat)) * pa_c_bl_elb_milestone_length_lower)) /\ exists pa_q_bl_elb_milestone_length_lower_repeat_decoded. pa_b_bl_elb_milestone_length_lower = pa_q_bl_elb_milestone_length_lower_repeat_decoded * S ((S (pa_i_bl_elb_milestone_length_lower_repeat)) * pa_c_bl_elb_milestone_length_lower) + (2)))) /\ (exists pa_u_bl_elb_milestone_length_lower_product pa_v_bl_elb_milestone_length_lower_product. ((((exists pa_h_bl_elb_milestone_length_lower_product_start. pa_h_bl_elb_milestone_length_lower_product_start + S (1) = S ((S (0)) * pa_v_bl_elb_milestone_length_lower_product)) /\ exists pa_q_bl_elb_milestone_length_lower_product_start. pa_u_bl_elb_milestone_length_lower_product = pa_q_bl_elb_milestone_length_lower_product_start * S ((S (0)) * pa_v_bl_elb_milestone_length_lower_product) + (1))) /\ ((((exists pa_h_bl_elb_milestone_length_lower_product_terminal. pa_h_bl_elb_milestone_length_lower_product_terminal + S (ff_lower_bl_elb_milestone_length) = S ((S (ff_exponent_bl_elb_milestone_length)) * pa_v_bl_elb_milestone_length_lower_product)) /\ exists pa_q_bl_elb_milestone_length_lower_product_terminal. pa_u_bl_elb_milestone_length_lower_product = pa_q_bl_elb_milestone_length_lower_product_terminal * S ((S (ff_exponent_bl_elb_milestone_length)) * pa_v_bl_elb_milestone_length_lower_product) + (ff_lower_bl_elb_milestone_length))) /\ forall pa_i_bl_elb_milestone_length_lower_product. (exists pa_lt_bl_elb_milestone_length_lower_product_bound. pa_lt_bl_elb_milestone_length_lower_product_bound + S pa_i_bl_elb_milestone_length_lower_product = ff_exponent_bl_elb_milestone_length) -> exists pa_p_bl_elb_milestone_length_lower_product pa_r_bl_elb_milestone_length_lower_product pa_s_bl_elb_milestone_length_lower_product. ((((exists pa_h_bl_elb_milestone_length_lower_product_factor. pa_h_bl_elb_milestone_length_lower_product_factor + S (pa_p_bl_elb_milestone_length_lower_product) = S ((S (pa_i_bl_elb_milestone_length_lower_product)) * pa_c_bl_elb_milestone_length_lower)) /\ exists pa_q_bl_elb_milestone_length_lower_product_factor. pa_b_bl_elb_milestone_length_lower = pa_q_bl_elb_milestone_length_lower_product_factor * S ((S (pa_i_bl_elb_milestone_length_lower_product)) * pa_c_bl_elb_milestone_length_lower) + (pa_p_bl_elb_milestone_length_lower_product))) /\ ((((exists pa_h_bl_elb_milestone_length_lower_product_partial. pa_h_bl_elb_milestone_length_lower_product_partial + S (pa_r_bl_elb_milestone_length_lower_product) = S ((S (pa_i_bl_elb_milestone_length_lower_product)) * pa_v_bl_elb_milestone_length_lower_product)) /\ exists pa_q_bl_elb_milestone_length_lower_product_partial. pa_u_bl_elb_milestone_length_lower_product = pa_q_bl_elb_milestone_length_lower_product_partial * S ((S (pa_i_bl_elb_milestone_length_lower_product)) * pa_v_bl_elb_milestone_length_lower_product) + (pa_r_bl_elb_milestone_length_lower_product))) /\ ((((exists pa_h_bl_elb_milestone_length_lower_product_successor. pa_h_bl_elb_milestone_length_lower_product_successor + S (pa_s_bl_elb_milestone_length_lower_product) = S ((S (S pa_i_bl_elb_milestone_length_lower_product)) * pa_v_bl_elb_milestone_length_lower_product)) /\ exists pa_q_bl_elb_milestone_length_lower_product_successor. pa_u_bl_elb_milestone_length_lower_product = pa_q_bl_elb_milestone_length_lower_product_successor * S ((S (S pa_i_bl_elb_milestone_length_lower_product)) * pa_v_bl_elb_milestone_length_lower_product) + (pa_s_bl_elb_milestone_length_lower_product))) /\ pa_s_bl_elb_milestone_length_lower_product = pa_r_bl_elb_milestone_length_lower_product * pa_p_bl_elb_milestone_length_lower_product)))))))) /\ ((exists pa_b_bl_elb_milestone_length_upper pa_c_bl_elb_milestone_length_upper. ((forall pa_i_bl_elb_milestone_length_upper_repeat. (exists pa_lt_bl_elb_milestone_length_upper_repeat_bound. pa_lt_bl_elb_milestone_length_upper_repeat_bound + S pa_i_bl_elb_milestone_length_upper_repeat = ell) -> (((exists pa_h_bl_elb_milestone_length_upper_repeat_decoded. pa_h_bl_elb_milestone_length_upper_repeat_decoded + S (2) = S ((S (pa_i_bl_elb_milestone_length_upper_repeat)) * pa_c_bl_elb_milestone_length_upper)) /\ exists pa_q_bl_elb_milestone_length_upper_repeat_decoded. pa_b_bl_elb_milestone_length_upper = pa_q_bl_elb_milestone_length_upper_repeat_decoded * S ((S (pa_i_bl_elb_milestone_length_upper_repeat)) * pa_c_bl_elb_milestone_length_upper) + (2)))) /\ (exists pa_u_bl_elb_milestone_length_upper_product pa_v_bl_elb_milestone_length_upper_product. ((((exists pa_h_bl_elb_milestone_length_upper_product_start. pa_h_bl_elb_milestone_length_upper_product_start + S (1) = S ((S (0)) * pa_v_bl_elb_milestone_length_upper_product)) /\ exists pa_q_bl_elb_milestone_length_upper_product_start. pa_u_bl_elb_milestone_length_upper_product = pa_q_bl_elb_milestone_length_upper_product_start * S ((S (0)) * pa_v_bl_elb_milestone_length_upper_product) + (1))) /\ ((((exists pa_h_bl_elb_milestone_length_upper_product_terminal. pa_h_bl_elb_milestone_length_upper_product_terminal + S (ff_upper_bl_elb_milestone_length) = S ((S (ell)) * pa_v_bl_elb_milestone_length_upper_product)) /\ exists pa_q_bl_elb_milestone_length_upper_product_terminal. pa_u_bl_elb_milestone_length_upper_product = pa_q_bl_elb_milestone_length_upper_product_terminal * S ((S (ell)) * pa_v_bl_elb_milestone_length_upper_product) + (ff_upper_bl_elb_milestone_length))) /\ forall pa_i_bl_elb_milestone_length_upper_product. (exists pa_lt_bl_elb_milestone_length_upper_product_bound. pa_lt_bl_elb_milestone_length_upper_product_bound + S pa_i_bl_elb_milestone_length_upper_product = ell) -> exists pa_p_bl_elb_milestone_length_upper_product pa_r_bl_elb_milestone_length_upper_product pa_s_bl_elb_milestone_length_upper_product. ((((exists pa_h_bl_elb_milestone_length_upper_product_factor. pa_h_bl_elb_milestone_length_upper_product_factor + S (pa_p_bl_elb_milestone_length_upper_product) = S ((S (pa_i_bl_elb_milestone_length_upper_product)) * pa_c_bl_elb_milestone_length_upper)) /\ exists pa_q_bl_elb_milestone_length_upper_product_factor. pa_b_bl_elb_milestone_length_upper = pa_q_bl_elb_milestone_length_upper_product_factor * S ((S (pa_i_bl_elb_milestone_length_upper_product)) * pa_c_bl_elb_milestone_length_upper) + (pa_p_bl_elb_milestone_length_upper_product))) /\ ((((exists pa_h_bl_elb_milestone_length_upper_product_partial. pa_h_bl_elb_milestone_length_upper_product_partial + S (pa_r_bl_elb_milestone_length_upper_product) = S ((S (pa_i_bl_elb_milestone_length_upper_product)) * pa_v_bl_elb_milestone_length_upper_product)) /\ exists pa_q_bl_elb_milestone_length_upper_product_partial. pa_u_bl_elb_milestone_length_upper_product = pa_q_bl_elb_milestone_length_upper_product_partial * S ((S (pa_i_bl_elb_milestone_length_upper_product)) * pa_v_bl_elb_milestone_length_upper_product) + (pa_r_bl_elb_milestone_length_upper_product))) /\ ((((exists pa_h_bl_elb_milestone_length_upper_product_successor. pa_h_bl_elb_milestone_length_upper_product_successor + S (pa_s_bl_elb_milestone_length_upper_product) = S ((S (S pa_i_bl_elb_milestone_length_upper_product)) * pa_v_bl_elb_milestone_length_upper_product)) /\ exists pa_q_bl_elb_milestone_length_upper_product_successor. pa_u_bl_elb_milestone_length_upper_product = pa_q_bl_elb_milestone_length_upper_product_successor * S ((S (S pa_i_bl_elb_milestone_length_upper_product)) * pa_v_bl_elb_milestone_length_upper_product) + (pa_s_bl_elb_milestone_length_upper_product))) /\ pa_s_bl_elb_milestone_length_upper_product = pa_r_bl_elb_milestone_length_upper_product * pa_p_bl_elb_milestone_length_upper_product)))))))) /\ ((exists ff_lower_gap_bl_elb_milestone_length. ff_lower_gap_bl_elb_milestone_length + (ff_lower_bl_elb_milestone_length) = (b)) /\ (exists ff_upper_gap_bl_elb_milestone_length. ff_upper_gap_bl_elb_milestone_length + S (b) = (ff_upper_bl_elb_milestone_length))))))))) /\ ((exists egt_list_elb_milestone_execution egt_history_elb_milestone_execution egt_scale_elb_milestone_execution. ((exists cf_gcd_egt_elb_milestone_execution_trace. ((((exists ff_h_cf_egt_elb_milestone_execution_trace_initial_state. ff_h_cf_egt_elb_milestone_execution_trace_initial_state + S (((cf_gcd_egt_elb_milestone_execution_trace) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) * S ((cf_gcd_egt_elb_milestone_execution_trace) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) + ((((0) + (0)) * S ((0) + (0)) + ((0) + (0))) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0))))) = S ((S (0)) * egt_scale_elb_milestone_execution)) /\ exists ff_q_cf_egt_elb_milestone_execution_trace_initial_state. egt_history_elb_milestone_execution = ff_q_cf_egt_elb_milestone_execution_trace_initial_state * S ((S (0)) * egt_scale_elb_milestone_execution) + (((cf_gcd_egt_elb_milestone_execution_trace) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) * S ((cf_gcd_egt_elb_milestone_execution_trace) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) + ((((0) + (0)) * S ((0) + (0)) + ((0) + (0))) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0))))))) /\ ((((exists ff_h_cf_egt_elb_milestone_execution_trace_terminal_state. ff_h_cf_egt_elb_milestone_execution_trace_terminal_state + S (((a) + (((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution)))) * S ((a) + (((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution)))) + ((((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution))) + (((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution))))) = S ((S (k)) * egt_scale_elb_milestone_execution)) /\ exists ff_q_cf_egt_elb_milestone_execution_trace_terminal_state. egt_history_elb_milestone_execution = ff_q_cf_egt_elb_milestone_execution_trace_terminal_state * S ((S (k)) * egt_scale_elb_milestone_execution) + (((a) + (((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution)))) * S ((a) + (((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution)))) + ((((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution))) + (((b) + (egt_list_elb_milestone_execution)) * S ((b) + (egt_list_elb_milestone_execution)) + ((egt_list_elb_milestone_execution) + (egt_list_elb_milestone_execution))))))) /\ forall cf_index_egt_elb_milestone_execution_trace. (exists ff_lt_cf_egt_elb_milestone_execution_trace_index. ff_lt_cf_egt_elb_milestone_execution_trace_index + S cf_index_egt_elb_milestone_execution_trace = k) -> exists cf_old_a_egt_elb_milestone_execution_trace cf_old_b_egt_elb_milestone_execution_trace cf_tail_egt_elb_milestone_execution_trace cf_new_a_egt_elb_milestone_execution_trace cf_new_b_egt_elb_milestone_execution_trace cf_head_egt_elb_milestone_execution_trace cf_quotient_egt_elb_milestone_execution_trace. ((((exists ff_h_cf_egt_elb_milestone_execution_trace_previous_state. ff_h_cf_egt_elb_milestone_execution_trace_previous_state + S (((cf_old_a_egt_elb_milestone_execution_trace) + (((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)))) * S ((cf_old_a_egt_elb_milestone_execution_trace) + (((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)))) + ((((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace))) + (((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace))))) = S ((S (cf_index_egt_elb_milestone_execution_trace)) * egt_scale_elb_milestone_execution)) /\ exists ff_q_cf_egt_elb_milestone_execution_trace_previous_state. egt_history_elb_milestone_execution = ff_q_cf_egt_elb_milestone_execution_trace_previous_state * S ((S (cf_index_egt_elb_milestone_execution_trace)) * egt_scale_elb_milestone_execution) + (((cf_old_a_egt_elb_milestone_execution_trace) + (((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)))) * S ((cf_old_a_egt_elb_milestone_execution_trace) + (((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)))) + ((((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace))) + (((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) * S ((cf_old_b_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace)) + ((cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace))))))) /\ ((((exists ff_h_cf_egt_elb_milestone_execution_trace_following_state. ff_h_cf_egt_elb_milestone_execution_trace_following_state + S (((cf_new_a_egt_elb_milestone_execution_trace) + (((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)))) * S ((cf_new_a_egt_elb_milestone_execution_trace) + (((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)))) + ((((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace))) + (((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace))))) = S ((S (S cf_index_egt_elb_milestone_execution_trace)) * egt_scale_elb_milestone_execution)) /\ exists ff_q_cf_egt_elb_milestone_execution_trace_following_state. egt_history_elb_milestone_execution = ff_q_cf_egt_elb_milestone_execution_trace_following_state * S ((S (S cf_index_egt_elb_milestone_execution_trace)) * egt_scale_elb_milestone_execution) + (((cf_new_a_egt_elb_milestone_execution_trace) + (((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)))) * S ((cf_new_a_egt_elb_milestone_execution_trace) + (((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)))) + ((((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace))) + (((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) * S ((cf_new_b_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace)) + ((cf_head_egt_elb_milestone_execution_trace) + (cf_head_egt_elb_milestone_execution_trace))))))) /\ (cf_new_b_egt_elb_milestone_execution_trace = cf_old_a_egt_elb_milestone_execution_trace /\ (cf_new_a_egt_elb_milestone_execution_trace = cf_new_b_egt_elb_milestone_execution_trace * cf_quotient_egt_elb_milestone_execution_trace + cf_old_b_egt_elb_milestone_execution_trace /\ ((exists ff_lt_cf_egt_elb_milestone_execution_trace_remainder. ff_lt_cf_egt_elb_milestone_execution_trace_remainder + S cf_old_b_egt_elb_milestone_execution_trace = cf_new_b_egt_elb_milestone_execution_trace) /\ (cf_head_egt_elb_milestone_execution_trace = S ((cf_quotient_egt_elb_milestone_execution_trace + cf_tail_egt_elb_milestone_execution_trace) * S (cf_quotient_egt_elb_milestone_execution_trace + cf_tail_egt_elb_milestone_execution_trace) + (cf_tail_egt_elb_milestone_execution_trace + cf_tail_egt_elb_milestone_execution_trace))))))))))) /\ ((((exists ff_h_cf_egt_elb_milestone_execution_initial_state. ff_h_cf_egt_elb_milestone_execution_initial_state + S (((g) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) * S ((g) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) + ((((0) + (0)) * S ((0) + (0)) + ((0) + (0))) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0))))) = S ((S (0)) * egt_scale_elb_milestone_execution)) /\ exists ff_q_cf_egt_elb_milestone_execution_initial_state. egt_history_elb_milestone_execution = ff_q_cf_egt_elb_milestone_execution_initial_state * S ((S (0)) * egt_scale_elb_milestone_execution) + (((g) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) * S ((g) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0)))) + ((((0) + (0)) * S ((0) + (0)) + ((0) + (0))) + (((0) + (0)) * S ((0) + (0)) + ((0) + (0))))))) /\ ((((exists ec_gcd_left_egt_elb_milestone_execution_result. a = g * ec_gcd_left_egt_elb_milestone_execution_result) /\ (exists ec_gcd_right_egt_elb_milestone_execution_result. b = g * ec_gcd_right_egt_elb_milestone_execution_result)) /\ forall ec_gcd_common_egt_elb_milestone_execution_result. (exists ec_gcd_common_left_egt_elb_milestone_execution_result. a = ec_gcd_common_egt_elb_milestone_execution_result * ec_gcd_common_left_egt_elb_milestone_execution_result) -> (exists ec_gcd_common_right_egt_elb_milestone_execution_result. b = ec_gcd_common_egt_elb_milestone_execution_result * ec_gcd_common_right_egt_elb_milestone_execution_result) -> exists ec_gcd_greatest_egt_elb_milestone_execution_result. g = ec_gcd_common_egt_elb_milestone_execution_result * ec_gcd_greatest_egt_elb_milestone_execution_result))))) /\ exists elb_bound_gap_milestone. elb_bound_gap_milestone + k = 2 * ell + 1))

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