Factorial

Readable signature

Factorial(n, z)

Exact expansion

exists ff_b_defined_factorial ff_c_defined_factorial. ((forall ff_i_defined_factorial_range. (exists ff_lt_defined_factorial_range_bound. ff_lt_defined_factorial_range_bound + S ff_i_defined_factorial_range = n) -> (((exists ff_h_defined_factorial_range_decoded. ff_h_defined_factorial_range_decoded + S (1 + ff_i_defined_factorial_range) = S ((S (ff_i_defined_factorial_range)) * ff_c_defined_factorial)) /\ exists ff_q_defined_factorial_range_decoded. ff_b_defined_factorial = ff_q_defined_factorial_range_decoded * S ((S (ff_i_defined_factorial_range)) * ff_c_defined_factorial) + (1 + ff_i_defined_factorial_range)))) /\ (exists ff_u_defined_factorial_product ff_v_defined_factorial_product. ((((exists ff_h_defined_factorial_product_start. ff_h_defined_factorial_product_start + S (1) = S ((S (0)) * ff_v_defined_factorial_product)) /\ exists ff_q_defined_factorial_product_start. ff_u_defined_factorial_product = ff_q_defined_factorial_product_start * S ((S (0)) * ff_v_defined_factorial_product) + (1))) /\ ((((exists ff_h_defined_factorial_product_terminal. ff_h_defined_factorial_product_terminal + S (z) = S ((S (n)) * ff_v_defined_factorial_product)) /\ exists ff_q_defined_factorial_product_terminal. ff_u_defined_factorial_product = ff_q_defined_factorial_product_terminal * S ((S (n)) * ff_v_defined_factorial_product) + (z))) /\ forall ff_i_defined_factorial_product. (exists ff_lt_defined_factorial_product_bound. ff_lt_defined_factorial_product_bound + S ff_i_defined_factorial_product = n) -> exists ff_p_defined_factorial_product ff_r_defined_factorial_product ff_s_defined_factorial_product. ((((exists ff_h_defined_factorial_product_factor. ff_h_defined_factorial_product_factor + S (ff_p_defined_factorial_product) = S ((S (ff_i_defined_factorial_product)) * ff_c_defined_factorial)) /\ exists ff_q_defined_factorial_product_factor. ff_b_defined_factorial = ff_q_defined_factorial_product_factor * S ((S (ff_i_defined_factorial_product)) * ff_c_defined_factorial) + (ff_p_defined_factorial_product))) /\ ((((exists ff_h_defined_factorial_product_partial. ff_h_defined_factorial_product_partial + S (ff_r_defined_factorial_product) = S ((S (ff_i_defined_factorial_product)) * ff_v_defined_factorial_product)) /\ exists ff_q_defined_factorial_product_partial. ff_u_defined_factorial_product = ff_q_defined_factorial_product_partial * S ((S (ff_i_defined_factorial_product)) * ff_v_defined_factorial_product) + (ff_r_defined_factorial_product))) /\ ((((exists ff_h_defined_factorial_product_successor. ff_h_defined_factorial_product_successor + S (ff_s_defined_factorial_product) = S ((S (S ff_i_defined_factorial_product)) * ff_v_defined_factorial_product)) /\ exists ff_q_defined_factorial_product_successor. ff_u_defined_factorial_product = ff_q_defined_factorial_product_successor * S ((S (S ff_i_defined_factorial_product)) * ff_v_defined_factorial_product) + (ff_s_defined_factorial_product))) /\ ff_s_defined_factorial_product = ff_r_defined_factorial_product * ff_p_defined_factorial_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

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Reviewed Factorial corresponds to blueprint Fact with checked argument positions [0, 1].

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.