BinaryExecutionOperationCount(b,c,ell,k)

Hygienic expanded first-order definition

exists ff_ones_bd_milestone. ((((exists ff_u_bd_milestone_count_sum ff_v_bd_milestone_count_sum. ((((exists ff_h_bd_milestone_count_sum_start. ff_h_bd_milestone_count_sum_start + S (0) = S ((S (0)) * ff_v_bd_milestone_count_sum)) /\ exists ff_q_bd_milestone_count_sum_start. ff_u_bd_milestone_count_sum = ff_q_bd_milestone_count_sum_start * S ((S (0)) * ff_v_bd_milestone_count_sum) + (0))) /\ ((((exists ff_h_bd_milestone_count_sum_terminal. ff_h_bd_milestone_count_sum_terminal + S (ff_ones_bd_milestone) = S ((S (ell)) * ff_v_bd_milestone_count_sum)) /\ exists ff_q_bd_milestone_count_sum_terminal. ff_u_bd_milestone_count_sum = ff_q_bd_milestone_count_sum_terminal * S ((S (ell)) * ff_v_bd_milestone_count_sum) + (ff_ones_bd_milestone))) /\ forall ff_i_bd_milestone_count_sum. (exists ff_lt_bd_milestone_count_sum_bound. ff_lt_bd_milestone_count_sum_bound + S ff_i_bd_milestone_count_sum = ell) -> exists ff_a_bd_milestone_count_sum ff_r_bd_milestone_count_sum ff_s_bd_milestone_count_sum. ((((exists ff_h_bd_milestone_count_sum_summand. ff_h_bd_milestone_count_sum_summand + S (ff_a_bd_milestone_count_sum) = S ((S (ff_i_bd_milestone_count_sum)) * c)) /\ exists ff_q_bd_milestone_count_sum_summand. b = ff_q_bd_milestone_count_sum_summand * S ((S (ff_i_bd_milestone_count_sum)) * c) + (ff_a_bd_milestone_count_sum))) /\ ((((exists ff_h_bd_milestone_count_sum_partial. ff_h_bd_milestone_count_sum_partial + S (ff_r_bd_milestone_count_sum) = S ((S (ff_i_bd_milestone_count_sum)) * ff_v_bd_milestone_count_sum)) /\ exists ff_q_bd_milestone_count_sum_partial. ff_u_bd_milestone_count_sum = ff_q_bd_milestone_count_sum_partial * S ((S (ff_i_bd_milestone_count_sum)) * ff_v_bd_milestone_count_sum) + (ff_r_bd_milestone_count_sum))) /\ ((((exists ff_h_bd_milestone_count_sum_successor. ff_h_bd_milestone_count_sum_successor + S (ff_s_bd_milestone_count_sum) = S ((S (S ff_i_bd_milestone_count_sum)) * ff_v_bd_milestone_count_sum)) /\ exists ff_q_bd_milestone_count_sum_successor. ff_u_bd_milestone_count_sum = ff_q_bd_milestone_count_sum_successor * S ((S (S ff_i_bd_milestone_count_sum)) * ff_v_bd_milestone_count_sum) + (ff_s_bd_milestone_count_sum))) /\ ff_s_bd_milestone_count_sum = ff_r_bd_milestone_count_sum + ff_a_bd_milestone_count_sum)))))) /\ (forall ff_i_bd_milestone_count_bits. (exists ff_lt_bd_milestone_count_bits_bound. ff_lt_bd_milestone_count_bits_bound + S ff_i_bd_milestone_count_bits = ell) -> exists ff_bit_bd_milestone_count_bits. ((((exists ff_h_bd_milestone_count_bits_decoded. ff_h_bd_milestone_count_bits_decoded + S (ff_bit_bd_milestone_count_bits) = S ((S (ff_i_bd_milestone_count_bits)) * c)) /\ exists ff_q_bd_milestone_count_bits_decoded. b = ff_q_bd_milestone_count_bits_decoded * S ((S (ff_i_bd_milestone_count_bits)) * c) + (ff_bit_bd_milestone_count_bits))) /\ (ff_bit_bd_milestone_count_bits = 0 \/ ff_bit_bd_milestone_count_bits = 1))))) /\ k = (2 + (ell + ell)) + ff_ones_bd_milestone)

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