PowerQuotPrefix

Readable signature

PowerQuotPrefix(p,n,b,c,l)

Exact expansion

forall bls_index_bertrand_defined_power_quotients. (exists bls_gap_bertrand_defined_power_quotients_bound. bls_gap_bertrand_defined_power_quotients_bound + S (bls_index_bertrand_defined_power_quotients) = (l)) -> exists bls_power_bertrand_defined_power_quotients bls_quotient_bertrand_defined_power_quotients bls_remainder_bertrand_defined_power_quotients. ((exists bpvi_b_bls_bertrand_defined_power_quotients_power bpvi_c_bls_bertrand_defined_power_quotients_power. ((forall bpvi_i_bls_bertrand_defined_power_quotients_power. (exists bpvi_repeat_gap_bls_bertrand_defined_power_quotients_power. bpvi_repeat_gap_bls_bertrand_defined_power_quotients_power + S bpvi_i_bls_bertrand_defined_power_quotients_power = S bls_index_bertrand_defined_power_quotients) -> (((exists bpvi_h_bls_bertrand_defined_power_quotients_power_repeat. bpvi_h_bls_bertrand_defined_power_quotients_power_repeat + S (p) = S ((S (bpvi_i_bls_bertrand_defined_power_quotients_power)) * bpvi_c_bls_bertrand_defined_power_quotients_power)) /\ exists bpvi_q_bls_bertrand_defined_power_quotients_power_repeat. bpvi_b_bls_bertrand_defined_power_quotients_power = bpvi_q_bls_bertrand_defined_power_quotients_power_repeat * S ((S (bpvi_i_bls_bertrand_defined_power_quotients_power)) * bpvi_c_bls_bertrand_defined_power_quotients_power) + (p)))) /\ (exists bpvi_u_bls_bertrand_defined_power_quotients_power bpvi_v_bls_bertrand_defined_power_quotients_power. ((((exists bpvi_h_bls_bertrand_defined_power_quotients_power_start. bpvi_h_bls_bertrand_defined_power_quotients_power_start + S (1) = S ((S (0)) * bpvi_v_bls_bertrand_defined_power_quotients_power)) /\ exists bpvi_q_bls_bertrand_defined_power_quotients_power_start. bpvi_u_bls_bertrand_defined_power_quotients_power = bpvi_q_bls_bertrand_defined_power_quotients_power_start * S ((S (0)) * bpvi_v_bls_bertrand_defined_power_quotients_power) + (1))) /\ ((((exists bpvi_h_bls_bertrand_defined_power_quotients_power_terminal. bpvi_h_bls_bertrand_defined_power_quotients_power_terminal + S (bls_power_bertrand_defined_power_quotients) = S ((S (S bls_index_bertrand_defined_power_quotients)) * bpvi_v_bls_bertrand_defined_power_quotients_power)) /\ exists bpvi_q_bls_bertrand_defined_power_quotients_power_terminal. bpvi_u_bls_bertrand_defined_power_quotients_power = bpvi_q_bls_bertrand_defined_power_quotients_power_terminal * S ((S (S bls_index_bertrand_defined_power_quotients)) * bpvi_v_bls_bertrand_defined_power_quotients_power) + (bls_power_bertrand_defined_power_quotients))) /\ forall bpvi_j_bls_bertrand_defined_power_quotients_power. (exists bpvi_product_gap_bls_bertrand_defined_power_quotients_power. bpvi_product_gap_bls_bertrand_defined_power_quotients_power + S bpvi_j_bls_bertrand_defined_power_quotients_power = S bls_index_bertrand_defined_power_quotients) -> exists bpvi_factor_bls_bertrand_defined_power_quotients_power bpvi_partial_bls_bertrand_defined_power_quotients_power bpvi_successor_bls_bertrand_defined_power_quotients_power. ((((exists bpvi_h_bls_bertrand_defined_power_quotients_power_factor. bpvi_h_bls_bertrand_defined_power_quotients_power_factor + S (bpvi_factor_bls_bertrand_defined_power_quotients_power) = S ((S (bpvi_j_bls_bertrand_defined_power_quotients_power)) * bpvi_c_bls_bertrand_defined_power_quotients_power)) /\ exists bpvi_q_bls_bertrand_defined_power_quotients_power_factor. bpvi_b_bls_bertrand_defined_power_quotients_power = bpvi_q_bls_bertrand_defined_power_quotients_power_factor * S ((S (bpvi_j_bls_bertrand_defined_power_quotients_power)) * bpvi_c_bls_bertrand_defined_power_quotients_power) + (bpvi_factor_bls_bertrand_defined_power_quotients_power))) /\ ((((exists bpvi_h_bls_bertrand_defined_power_quotients_power_partial. bpvi_h_bls_bertrand_defined_power_quotients_power_partial + S (bpvi_partial_bls_bertrand_defined_power_quotients_power) = S ((S (bpvi_j_bls_bertrand_defined_power_quotients_power)) * bpvi_v_bls_bertrand_defined_power_quotients_power)) /\ exists bpvi_q_bls_bertrand_defined_power_quotients_power_partial. bpvi_u_bls_bertrand_defined_power_quotients_power = bpvi_q_bls_bertrand_defined_power_quotients_power_partial * S ((S (bpvi_j_bls_bertrand_defined_power_quotients_power)) * bpvi_v_bls_bertrand_defined_power_quotients_power) + (bpvi_partial_bls_bertrand_defined_power_quotients_power))) /\ ((((exists bpvi_h_bls_bertrand_defined_power_quotients_power_successor. bpvi_h_bls_bertrand_defined_power_quotients_power_successor + S (bpvi_successor_bls_bertrand_defined_power_quotients_power) = S ((S (S bpvi_j_bls_bertrand_defined_power_quotients_power)) * bpvi_v_bls_bertrand_defined_power_quotients_power)) /\ exists bpvi_q_bls_bertrand_defined_power_quotients_power_successor. bpvi_u_bls_bertrand_defined_power_quotients_power = bpvi_q_bls_bertrand_defined_power_quotients_power_successor * S ((S (S bpvi_j_bls_bertrand_defined_power_quotients_power)) * bpvi_v_bls_bertrand_defined_power_quotients_power) + (bpvi_successor_bls_bertrand_defined_power_quotients_power))) /\ bpvi_successor_bls_bertrand_defined_power_quotients_power = bpvi_partial_bls_bertrand_defined_power_quotients_power * bpvi_factor_bls_bertrand_defined_power_quotients_power)))))))) /\ ((((exists ff_h_bls_bertrand_defined_power_quotients_quotient_entry. ff_h_bls_bertrand_defined_power_quotients_quotient_entry + S (bls_quotient_bertrand_defined_power_quotients) = S ((S (bls_index_bertrand_defined_power_quotients)) * c)) /\ exists ff_q_bls_bertrand_defined_power_quotients_quotient_entry. b = ff_q_bls_bertrand_defined_power_quotients_quotient_entry * S ((S (bls_index_bertrand_defined_power_quotients)) * c) + (bls_quotient_bertrand_defined_power_quotients))) /\ ((n = bls_power_bertrand_defined_power_quotients * bls_quotient_bertrand_defined_power_quotients + bls_remainder_bertrand_defined_power_quotients /\ exists bls_remainder_gap_bertrand_defined_power_quotients_division. bls_remainder_gap_bertrand_defined_power_quotients_division + S (bls_remainder_bertrand_defined_power_quotients) = bls_power_bertrand_defined_power_quotients))))

This node is conservative notation, not a theorem, new axiom, predicate constant, or kernel rule. Its expansion is checked for exact first-order AST equivalence.

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