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_scale_index_bottomlayer. ∀ eu_scale_source_bottomlayer. ∀ eu_scale_target_bottomlayer. Lt(eu_scale_index_bottomlayer,l) → BetaAt(b,c,eu_scale_index_bottomlayer,eu_scale_source_bottomlayer) → BetaAt(d,e,eu_scale_index_bottomlayer,eu_scale_target_bottomlayer) → (Coprime(eu_scale_index_bottomlayer,m) → ModEq(m,a · eu_scale_source_bottomlayer,eu_scale_target_bottomlayer)) ∧ (¬Coprime(eu_scale_index_bottomlayer,m) → ModEq(m,eu_scale_source_bottomlayer,eu_scale_target_bottomlayer))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall eu_scale_index_bottomlayer eu_scale_source_bottomlayer eu_scale_target_bottomlayer. (exists eut_gap_eu_bottomlayer_index. eut_gap_eu_bottomlayer_index + S (eu_scale_index_bottomlayer) = ((l))) -> (((exists fs_h_eu_bottomlayer_source. fs_h_eu_bottomlayer_source + S (eu_scale_source_bottomlayer) = S ((S (eu_scale_index_bottomlayer)) * (c))) /\ exists fs_q_eu_bottomlayer_source. (b) = fs_q_eu_bottomlayer_source * S ((S (eu_scale_index_bottomlayer)) * (c)) + (eu_scale_source_bottomlayer))) -> (((exists fs_h_eu_bottomlayer_target. fs_h_eu_bottomlayer_target + S (eu_scale_target_bottomlayer) = S ((S (eu_scale_index_bottomlayer)) * (e))) /\ exists fs_q_eu_bottomlayer_target. (d) = fs_q_eu_bottomlayer_target * S ((S (eu_scale_index_bottomlayer)) * (e)) + (eu_scale_target_bottomlayer))) -> (((forall eut_divisor_eu_bottomlayer_unit. (exists eut_left_eu_bottomlayer_unit. (eu_scale_index_bottomlayer) = eut_divisor_eu_bottomlayer_unit * eut_left_eu_bottomlayer_unit) -> (exists eut_right_eu_bottomlayer_unit. ((m)) = eut_divisor_eu_bottomlayer_unit * eut_right_eu_bottomlayer_unit) -> eut_divisor_eu_bottomlayer_unit = 1) -> (exists eu_mod_left_bottomlayer_scaled eu_mod_right_bottomlayer_scaled. (((a))*eu_scale_source_bottomlayer) + ((m)) * eu_mod_left_bottomlayer_scaled = (eu_scale_target_bottomlayer) + ((m)) * eu_mod_right_bottomlayer_scaled)) /\ (~(forall eut_divisor_eu_bottomlayer_unit. (exists eut_left_eu_bottomlayer_unit. (eu_scale_index_bottomlayer) = eut_divisor_eu_bottomlayer_unit * eut_left_eu_bottomlayer_unit) -> (exists eut_right_eu_bottomlayer_unit. ((m)) = eut_divisor_eu_bottomlayer_unit * eut_right_eu_bottomlayer_unit) -> eut_divisor_eu_bottomlayer_unit = 1) -> (exists eu_mod_left_bottomlayer_unchanged eu_mod_right_bottomlayer_unchanged. (eu_scale_source_bottomlayer) + ((m)) * eu_mod_left_bottomlayer_unchanged = (eu_scale_target_bottomlayer) + ((m)) * eu_mod_right_bottomlayer_unchanged)))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