Sum

Readable signature

Sum(b, c, l, z)

Exact expansion

exists ff_u_defined_sum ff_v_defined_sum. ((((exists ff_h_defined_sum_start. ff_h_defined_sum_start + S (0) = S ((S (0)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_start. ff_u_defined_sum = ff_q_defined_sum_start * S ((S (0)) * ff_v_defined_sum) + (0))) /\ ((((exists ff_h_defined_sum_terminal. ff_h_defined_sum_terminal + S (z) = S ((S (l)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_terminal. ff_u_defined_sum = ff_q_defined_sum_terminal * S ((S (l)) * ff_v_defined_sum) + (z))) /\ forall ff_i_defined_sum. (exists ff_lt_defined_sum_bound. ff_lt_defined_sum_bound + S ff_i_defined_sum = l) -> exists ff_a_defined_sum ff_r_defined_sum ff_s_defined_sum. ((((exists ff_h_defined_sum_summand. ff_h_defined_sum_summand + S (ff_a_defined_sum) = S ((S (ff_i_defined_sum)) * c)) /\ exists ff_q_defined_sum_summand. b = ff_q_defined_sum_summand * S ((S (ff_i_defined_sum)) * c) + (ff_a_defined_sum))) /\ ((((exists ff_h_defined_sum_partial. ff_h_defined_sum_partial + S (ff_r_defined_sum) = S ((S (ff_i_defined_sum)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_partial. ff_u_defined_sum = ff_q_defined_sum_partial * S ((S (ff_i_defined_sum)) * ff_v_defined_sum) + (ff_r_defined_sum))) /\ ((((exists ff_h_defined_sum_successor. ff_h_defined_sum_successor + S (ff_s_defined_sum) = S ((S (S ff_i_defined_sum)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_successor. ff_u_defined_sum = ff_q_defined_sum_successor * S ((S (S ff_i_defined_sum)) * ff_v_defined_sum) + (ff_s_defined_sum))) /\ ff_s_defined_sum = ff_r_defined_sum + ff_a_defined_sum)))))

This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.

Definition neighborhood

Depends on conservative definitions

Used by conservative definitions

All transitive conservative prerequisites

Used by theorem statements or local proof propositions

Grand-campaign planning vocabulary

Locate BetaSum in the global campaign vocabulary →

Reviewed Sum corresponds to blueprint BetaSum with checked argument positions [0, 1, 2, 3].

The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.