Exact expanded first-order arithmetic statement
forall p n b c k. (~((p) = 1) /\ forall pvs_left_jordan_base pvs_right_jordan_base. (p) = pvs_left_jordan_base * pvs_right_jordan_base -> pvs_left_jordan_base = 1 \/ pvs_right_jordan_base = 1) -> (exists jt_factor_jordan_modulus. (n)=(p)*jt_factor_jordan_modulus) -> (forall jt_divisor_power_primitive. (exists jt_factor_power_primitivemodulus. (n)=(jt_divisor_power_primitive)*jt_factor_power_primitivemodulus) -> (forall jt_index_power_primitivecoordinates jt_value_power_primitivecoordinates. (exists jt_gap_power_primitivecoordinatesindex. jt_gap_power_primitivecoordinatesindex+S (jt_index_power_primitivecoordinates)=(k)) -> (((exists fs_h_jt_power_primitivecoordinatesat. fs_h_jt_power_primitivecoordinatesat + S (jt_value_power_primitivecoordinates) = S ((S (jt_index_power_primitivecoordinates)) * c)) /\ exists fs_q_jt_power_primitivecoordinatesat. b = fs_q_jt_power_primitivecoordinatesat * S ((S (jt_index_power_primitivecoordinates)) * c) + (jt_value_power_primitivecoordinates))) -> (exists jt_factor_power_primitivecoordinatesdivides. (jt_value_power_primitivecoordinates)=(jt_divisor_power_primitive)*jt_factor_power_primitivecoordinatesdivides)) -> jt_divisor_power_primitive=1) -> ~(forall jt_index_power_all_divisible jt_value_power_all_divisible. (exists jt_gap_power_all_divisibleindex. jt_gap_power_all_divisibleindex+S (jt_index_power_all_divisible)=(k)) -> (((exists fs_h_jt_power_all_divisibleat. fs_h_jt_power_all_divisibleat + S (jt_value_power_all_divisible) = S ((S (jt_index_power_all_divisible)) * c)) /\ exists fs_q_jt_power_all_divisibleat. b = fs_q_jt_power_all_divisibleat * S ((S (jt_index_power_all_divisible)) * c) + (jt_value_power_all_divisible))) -> (exists jt_factor_power_all_divisibledivides. (jt_value_power_all_divisible)=(p)*jt_factor_power_all_divisibledivides))Constructive proof overview
Generated structural guide
A prime divisor of the modulus cannot divide every coordinate of a primitive tuple.
The unchanged tactic script uses 0 declared prerequisites and contains 15 exact native proof lines.
Alpha v35 checked-use · first admitted v35 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
01Fix variables and assumptionsL1–9
02Separate the logical casesL10–10
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L10
cases hp