Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Definition in prerequisite notation
∀ eu_index_bottomlayer. Lt(eu_index_bottomlayer,l) → ∃ x. BetaAt(b,c,eu_index_bottomlayer,x) ∧ CanonicalModularResidue(m,a · eu_index_bottomlayer,x)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall eu_index_bottomlayer. (exists eut_gap_eu_bottomlayer_index. eut_gap_eu_bottomlayer_index + S (eu_index_bottomlayer) = ((l))) -> exists eu_residue_bottomlayer. (((exists fs_h_eu_bottomlayer_at. fs_h_eu_bottomlayer_at + S (eu_residue_bottomlayer) = S ((S (eu_index_bottomlayer)) * (c))) /\ exists fs_q_eu_bottomlayer_at. (b) = fs_q_eu_bottomlayer_at * S ((S (eu_index_bottomlayer)) * (c)) + (eu_residue_bottomlayer))) /\ ((exists eut_gap_eu_bottomlayer_bound. eut_gap_eu_bottomlayer_bound + S (eu_residue_bottomlayer) = ((m))) /\ (exists eu_mod_left_bottomlayer_mod eu_mod_right_bottomlayer_mod. (((a))*eu_index_bottomlayer) + ((m)) * eu_mod_left_bottomlayer_mod = (eu_residue_bottomlayer) + ((m)) * eu_mod_right_bottomlayer_mod))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.
Direct definition dependencies
Definitions depending on this notation
none
Checked theorems using this definition
EU0007 · euler_multiplier_prefix_emptyEU0008 · euler_multiplier_prefix_extendEU0009 · euler_multiplier_prefix_existsEU000A · euler_multiplier_prefix_entryEU000B · euler_multiplier_prefix_bounded_injectiveEU000C · euler_multiplier_prefix_permutationEU000D · euler_multiplier_permutation_existsEU001B · euler_unit_product_reindex_scaleEU001F · euler_coprime_totient_power_value