BinaryExponentDigitCode(e,ell,b,c)

Hygienic expanded first-order definition

((forall ff_index_be_bd_milestone_digits ff_digit_be_bd_milestone_digits. (exists ff_lt_be_bd_milestone_digits_bound. ff_lt_be_bd_milestone_digits_bound + S ff_index_be_bd_milestone_digits = ell) -> (((exists ff_h_be_bd_milestone_digits_digit. ff_h_be_bd_milestone_digits_digit + S (ff_digit_be_bd_milestone_digits) = S ((S (ff_index_be_bd_milestone_digits)) * c)) /\ exists ff_q_be_bd_milestone_digits_digit. b = ff_q_be_bd_milestone_digits_digit * S ((S (ff_index_be_bd_milestone_digits)) * c) + (ff_digit_be_bd_milestone_digits))) -> (ff_digit_be_bd_milestone_digits = 0 \/ ff_digit_be_bd_milestone_digits = 1)) /\ (exists ff_u_ph_bd_milestone_horner ff_v_ph_bd_milestone_horner. ((((exists fs_h_ph_bd_milestone_horner_body_start. fs_h_ph_bd_milestone_horner_body_start + S (0) = S ((S (0)) * ff_v_ph_bd_milestone_horner)) /\ exists fs_q_ph_bd_milestone_horner_body_start. ff_u_ph_bd_milestone_horner = fs_q_ph_bd_milestone_horner_body_start * S ((S (0)) * ff_v_ph_bd_milestone_horner) + (0))) /\ ((((exists fs_h_ph_bd_milestone_horner_body_terminal. fs_h_ph_bd_milestone_horner_body_terminal + S (e) = S ((S (ell)) * ff_v_ph_bd_milestone_horner)) /\ exists fs_q_ph_bd_milestone_horner_body_terminal. ff_u_ph_bd_milestone_horner = fs_q_ph_bd_milestone_horner_body_terminal * S ((S (ell)) * ff_v_ph_bd_milestone_horner) + (e))) /\ forall ff_i_ph_bd_milestone_horner_body_steps. (exists ph_bound_bd_milestone_horner_body_steps. ph_bound_bd_milestone_horner_body_steps + S ff_i_ph_bd_milestone_horner_body_steps = ell) -> exists ff_coefficient_ph_bd_milestone_horner_body_steps ff_previous_ph_bd_milestone_horner_body_steps ff_current_ph_bd_milestone_horner_body_steps. ((((exists fs_h_ph_bd_milestone_horner_body_steps_coefficient. fs_h_ph_bd_milestone_horner_body_steps_coefficient + S (ff_coefficient_ph_bd_milestone_horner_body_steps) = S ((S (ff_i_ph_bd_milestone_horner_body_steps)) * c)) /\ exists fs_q_ph_bd_milestone_horner_body_steps_coefficient. b = fs_q_ph_bd_milestone_horner_body_steps_coefficient * S ((S (ff_i_ph_bd_milestone_horner_body_steps)) * c) + (ff_coefficient_ph_bd_milestone_horner_body_steps))) /\ ((((exists fs_h_ph_bd_milestone_horner_body_steps_before. fs_h_ph_bd_milestone_horner_body_steps_before + S (ff_previous_ph_bd_milestone_horner_body_steps) = S ((S (ff_i_ph_bd_milestone_horner_body_steps)) * ff_v_ph_bd_milestone_horner)) /\ exists fs_q_ph_bd_milestone_horner_body_steps_before. ff_u_ph_bd_milestone_horner = fs_q_ph_bd_milestone_horner_body_steps_before * S ((S (ff_i_ph_bd_milestone_horner_body_steps)) * ff_v_ph_bd_milestone_horner) + (ff_previous_ph_bd_milestone_horner_body_steps))) /\ ((((exists fs_h_ph_bd_milestone_horner_body_steps_after. fs_h_ph_bd_milestone_horner_body_steps_after + S (ff_current_ph_bd_milestone_horner_body_steps) = S ((S (S ff_i_ph_bd_milestone_horner_body_steps)) * ff_v_ph_bd_milestone_horner)) /\ exists fs_q_ph_bd_milestone_horner_body_steps_after. ff_u_ph_bd_milestone_horner = fs_q_ph_bd_milestone_horner_body_steps_after * S ((S (S ff_i_ph_bd_milestone_horner_body_steps)) * ff_v_ph_bd_milestone_horner) + (ff_current_ph_bd_milestone_horner_body_steps))) /\ ff_current_ph_bd_milestone_horner_body_steps = ff_previous_ph_bd_milestone_horner_body_steps * 2 + ff_coefficient_ph_bd_milestone_horner_body_steps)))))))

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