Exact expanded first-order arithmetic statement
forall d b c. forall jt_index_allempty jt_value_allempty. (exists jt_gap_allemptyindex. jt_gap_allemptyindex+S (jt_index_allempty)=(0)) -> (((exists fs_h_jt_allemptyat. fs_h_jt_allemptyat + S (jt_value_allempty) = S ((S (jt_index_allempty)) * c)) /\ exists fs_q_jt_allemptyat. b = fs_q_jt_allemptyat * S ((S (jt_index_allempty)) * c) + (jt_value_allempty))) -> (exists jt_factor_allemptydivides. (jt_value_allempty)=(d)*jt_factor_allemptydivides)Constructive proof overview
Generated structural guide
Every divisor vacuously divides all entries of an empty tuple.
The unchanged tactic script uses 2 declared prerequisites and contains 14 exact native proof lines.
Alpha v35 checked-use · first admitted v35 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
lt_not_le Alpha theorem; checked-use authorized zero_le Alpha theorem; checked-use authorizedDirect 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 assumptionsL1–7
02Separate the logical casesL8–8
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L8
exfalso