Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.
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Pow(a, e, z)Exact expansion
exists ff_b_defined_power ff_c_defined_power. ((forall ff_i_defined_power_repeat. (exists ff_lt_defined_power_repeat_bound. ff_lt_defined_power_repeat_bound + S ff_i_defined_power_repeat = e) -> (((exists ff_h_defined_power_repeat_decoded. ff_h_defined_power_repeat_decoded + S (a) = S ((S (ff_i_defined_power_repeat)) * ff_c_defined_power)) /\ exists ff_q_defined_power_repeat_decoded. ff_b_defined_power = ff_q_defined_power_repeat_decoded * S ((S (ff_i_defined_power_repeat)) * ff_c_defined_power) + (a)))) /\ (exists ff_u_defined_power_product ff_v_defined_power_product. ((((exists ff_h_defined_power_product_start. ff_h_defined_power_product_start + S (1) = S ((S (0)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_start. ff_u_defined_power_product = ff_q_defined_power_product_start * S ((S (0)) * ff_v_defined_power_product) + (1))) /\ ((((exists ff_h_defined_power_product_terminal. ff_h_defined_power_product_terminal + S (z) = S ((S (e)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_terminal. ff_u_defined_power_product = ff_q_defined_power_product_terminal * S ((S (e)) * ff_v_defined_power_product) + (z))) /\ forall ff_i_defined_power_product. (exists ff_lt_defined_power_product_bound. ff_lt_defined_power_product_bound + S ff_i_defined_power_product = e) -> exists ff_p_defined_power_product ff_r_defined_power_product ff_s_defined_power_product. ((((exists ff_h_defined_power_product_factor. ff_h_defined_power_product_factor + S (ff_p_defined_power_product) = S ((S (ff_i_defined_power_product)) * ff_c_defined_power)) /\ exists ff_q_defined_power_product_factor. ff_b_defined_power = ff_q_defined_power_product_factor * S ((S (ff_i_defined_power_product)) * ff_c_defined_power) + (ff_p_defined_power_product))) /\ ((((exists ff_h_defined_power_product_partial. ff_h_defined_power_product_partial + S (ff_r_defined_power_product) = S ((S (ff_i_defined_power_product)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_partial. ff_u_defined_power_product = ff_q_defined_power_product_partial * S ((S (ff_i_defined_power_product)) * ff_v_defined_power_product) + (ff_r_defined_power_product))) /\ ((((exists ff_h_defined_power_product_successor. ff_h_defined_power_product_successor + S (ff_s_defined_power_product) = S ((S (S ff_i_defined_power_product)) * ff_v_defined_power_product)) /\ exists ff_q_defined_power_product_successor. ff_u_defined_power_product = ff_q_defined_power_product_successor * S ((S (S ff_i_defined_power_product)) * ff_v_defined_power_product) + (ff_s_defined_power_product))) /\ ff_s_defined_power_product = ff_r_defined_power_product * ff_p_defined_power_product)))))))This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.
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Grand-campaign planning vocabulary
Locate Pow in the global campaign vocabulary →
Reviewed Pow corresponds to blueprint Pow with checked argument positions [0, 1, 2].
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.