Exact expanded first-order arithmetic statement
forall b c d e. forall jt_index_eqempty jt_left_eqempty jt_right_eqempty. (exists jt_gap_eqemptyindex. jt_gap_eqemptyindex+S (jt_index_eqempty)=(0)) -> (((exists fs_h_jt_eqemptyleft. fs_h_jt_eqemptyleft + S (jt_left_eqempty) = S ((S (jt_index_eqempty)) * c)) /\ exists fs_q_jt_eqemptyleft. b = fs_q_jt_eqemptyleft * S ((S (jt_index_eqempty)) * c) + (jt_left_eqempty))) -> (((exists fs_h_jt_eqemptyright. fs_h_jt_eqemptyright + S (jt_right_eqempty) = S ((S (jt_index_eqempty)) * e)) /\ exists fs_q_jt_eqemptyright. d = fs_q_jt_eqemptyright * S ((S (jt_index_eqempty)) * e) + (jt_right_eqempty))) -> jt_left_eqempty=jt_right_eqemptyConstructive proof overview
Generated structural guide
All actual empty tuples are coordinatewise equal.
The unchanged tactic script uses 2 declared prerequisites and contains 17 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 assumptionsL1–10
02Separate the logical casesL11–11
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L11
exfalso