Product

Readable signature

Product(b, c, l, z)

Exact expansion

exists ff_u_defined_product ff_v_defined_product. ((((exists ff_h_defined_product_start. ff_h_defined_product_start + S (1) = S ((S (0)) * ff_v_defined_product)) /\ exists ff_q_defined_product_start. ff_u_defined_product = ff_q_defined_product_start * S ((S (0)) * ff_v_defined_product) + (1))) /\ ((((exists ff_h_defined_product_terminal. ff_h_defined_product_terminal + S (z) = S ((S (l)) * ff_v_defined_product)) /\ exists ff_q_defined_product_terminal. ff_u_defined_product = ff_q_defined_product_terminal * S ((S (l)) * ff_v_defined_product) + (z))) /\ forall ff_i_defined_product. (exists ff_lt_defined_product_bound. ff_lt_defined_product_bound + S ff_i_defined_product = l) -> exists ff_p_defined_product ff_r_defined_product ff_s_defined_product. ((((exists ff_h_defined_product_factor. ff_h_defined_product_factor + S (ff_p_defined_product) = S ((S (ff_i_defined_product)) * c)) /\ exists ff_q_defined_product_factor. b = ff_q_defined_product_factor * S ((S (ff_i_defined_product)) * c) + (ff_p_defined_product))) /\ ((((exists ff_h_defined_product_partial. ff_h_defined_product_partial + S (ff_r_defined_product) = S ((S (ff_i_defined_product)) * ff_v_defined_product)) /\ exists ff_q_defined_product_partial. ff_u_defined_product = ff_q_defined_product_partial * S ((S (ff_i_defined_product)) * ff_v_defined_product) + (ff_r_defined_product))) /\ ((((exists ff_h_defined_product_successor. ff_h_defined_product_successor + S (ff_s_defined_product) = S ((S (S ff_i_defined_product)) * ff_v_defined_product)) /\ exists ff_q_defined_product_successor. ff_u_defined_product = ff_q_defined_product_successor * S ((S (S ff_i_defined_product)) * ff_v_defined_product) + (ff_s_defined_product))) /\ ff_s_defined_product = ff_r_defined_product * ff_p_defined_product)))))

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 Product in the global campaign vocabulary →

Reviewed Product corresponds to blueprint Product 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.