Exact expanded first-order arithmetic statement
forall a m. ((exists eut_gap_eu_unit_given_domain. eut_gap_eu_unit_given_domain + S (1) = (m)) /\ exists eu_inverse_unit_given. (exists eut_gap_eu_unit_given_bound. eut_gap_eu_unit_given_bound + S (eu_inverse_unit_given) = (m)) /\ (exists eu_mod_left_unit_given_inverse eu_mod_right_unit_given_inverse. ((a)*eu_inverse_unit_given) + (m) * eu_mod_left_unit_given_inverse = (1) + (m) * eu_mod_right_unit_given_inverse)) -> (forall eut_divisor_eu_unit_coprime. (exists eut_left_eu_unit_coprime. (a) = eut_divisor_eu_unit_coprime * eut_left_eu_unit_coprime) -> (exists eut_right_eu_unit_coprime. (m) = eut_divisor_eu_unit_coprime * eut_right_eu_unit_coprime) -> eut_divisor_eu_unit_coprime = 1)Constructive proof overview
Generated structural guide
An actual bounded inverse implies the frozen common-divisor coprimality graph.
The unchanged tactic script uses 1 declared prerequisite and contains 11 exact native proof lines.
Public research checkpoint: original HA and independently compiled Lean verified; not Alpha-enrolled, no Alpha checked-use authority; 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. The literal dependency-closed bundle is checked by original HA and the independently compiled Lean verifier. Public delivery grants no Alpha checked-use authority or 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.