beta_sum_zero

Exact expanded PA statement

forall b c n. (exists fs_u_zero fs_v_zero. ((((exists fs_h_zero_body_start. fs_h_zero_body_start + S (0) = S ((S (0)) * fs_v_zero)) /\ exists fs_q_zero_body_start. fs_u_zero = fs_q_zero_body_start * S ((S (0)) * fs_v_zero) + (0))) /\ ((((exists fs_h_zero_body_terminal. fs_h_zero_body_terminal + S (n) = S ((S (0)) * fs_v_zero)) /\ exists fs_q_zero_body_terminal. fs_u_zero = fs_q_zero_body_terminal * S ((S (0)) * fs_v_zero) + (n))) /\ forall fs_i_zero_body_steps. (exists fs_lt_zero_body_steps_bound. fs_lt_zero_body_steps_bound + S fs_i_zero_body_steps = 0) -> exists fs_a_zero_body_steps fs_r_zero_body_steps fs_s_zero_body_steps. ((((exists fs_h_zero_body_steps_summand. fs_h_zero_body_steps_summand + S (fs_a_zero_body_steps) = S ((S (fs_i_zero_body_steps)) * c)) /\ exists fs_q_zero_body_steps_summand. b = fs_q_zero_body_steps_summand * S ((S (fs_i_zero_body_steps)) * c) + (fs_a_zero_body_steps))) /\ ((((exists fs_h_zero_body_steps_partial. fs_h_zero_body_steps_partial + S (fs_r_zero_body_steps) = S ((S (fs_i_zero_body_steps)) * fs_v_zero)) /\ exists fs_q_zero_body_steps_partial. fs_u_zero = fs_q_zero_body_steps_partial * S ((S (fs_i_zero_body_steps)) * fs_v_zero) + (fs_r_zero_body_steps))) /\ ((((exists fs_h_zero_body_steps_successor. fs_h_zero_body_steps_successor + S (fs_s_zero_body_steps) = S ((S (S fs_i_zero_body_steps)) * fs_v_zero)) /\ exists fs_q_zero_body_steps_successor. fs_u_zero = fs_q_zero_body_steps_successor * S ((S (S fs_i_zero_body_steps)) * fs_v_zero) + (fs_s_zero_body_steps))) /\ fs_s_zero_body_steps = fs_r_zero_body_steps + fs_a_zero_body_steps)))))) -> n = 0